Modeling and Optimization: Theory and Applications

# Conference program

## Wednesday 16th of August 2017

7:30 8:15 Registration and breakfast
8:15 8:30 Welcome
8:30 9:30 Plenary talk
 Simple Reduction of Lemke's Solvable Linear Complementarity Problems to Bimatrix Games Ilan Adler abstract Simple Reduction of Lemke's Solvable Linear Complementarity Problems to Bimatrix Games Ilan Adler It is well known that many optimization problems, ranging from linear programming to hard combinatorial problems, as well as many engineering and economics problems, can be formulated as linear complementarity problems (LCP). One particular LCP, finding a Nash equilibrium of a bimatrix game (2-NASH), motivated the development of the elegant Simplex-like Lemke’s algorithm which is guaranteed to terminate in a finite number of iterations but not necessarily with a solution (or a certificate that no solution exists). Over the years, many subclasses of LCP, covering a variety of optimization problems, were proven to be solvable by Lemke’s algorithm. It turned out that, in general, Lemke solvable LCPs belong to the complexity class PPAD (Polynomial-time Parity Argument Directed) and that, quite surprisingly, 2 NASH is PPADcomplete. Thus, Lemke solvable LCPs can be formulated as 2 NASH. While of great theoretical value, the ingeniously constructed reduction (which is designed for all PPAD problem) is very complicated, difficult to implement, and not readily available for potential insights. In this talk, I’ll present and discuss a simple reduction of Lemke-solvable LCPs to bimatrix games that is easy to implement and have the potential to gain additional insights to problems (including several models of market equilibrium) for which the reduction is applicable.
9:30 9:45 Coffee break
9:45 11:15 Parallel technical sessions
11:15 11:30 Coffee break
11:30 12:30 Plenary talk
 The Geometry of the Simplex method: Diameters of Network-Flow Polytopes and Other Combinatorial Problems Jesus A. De Loera abstract The Geometry of the Simplex method: Diameters of Network-Flow Polytopes and Other Combinatorial Problems Jesus A. De Loera Linear programs (LPs) and their associated convex polyhedra are, without any doubt, at the core of both the theory and the practice of Mathematical Optimization (e.g., in discrete optimization LPs are used in practical computations using branch-and-bound, and in approximation algorithms, e.g., in rounding schemes). The simplex method is of course one of the most popular techniques to solve LPs but despite its key importance, many simple easy-to-state mathematical properties of the algorithm remain unknown, even for the network simplex method versions. Perhaps the most famous geometric-combinatorial challenge is to determine a worst-case upper bound for the graph diameter of polyhedra. Although a lot of progress has been made, today even for the most elementary textbook linear programs we remain ignorant as to what the exact diameter upper bounds are. In this talk, I will discuss this geometric problem and present the key ideas for proving that the diameter of graphs of all network-flow polytopes satisfy the Hirsch linear bound. This is joint work with S. Borgwardt (Univ of Colorado) and E. Finhold (Fraunhofer Institut).
12:30 13:30 Lunch
13:30 15:00 Parallel technical sessions
 Stochastic Optimization Semidefinite Programming Modeling Energy and Environmental Systems Topology Optimization Using Conditional Value at Risk Geoffrey Oxberry abstract Topology Optimization Using Conditional Value at Risk Geoffrey Oxberry Traditional approaches to formulating stochastic topology optimization problems for additive manufacturing tend to use linear combinations of the mean and standard deviation of a design figure of merit (e.g., compliance) in an approach called robust design optimization (RDO). However, this choice of objective/constraint underweights tail events for non-normal random variables. An alternate approach, called reliability-based design optimization (RBDO) changes the objective function (e.g., to minimize mass) and moves the design figure of merit into a chance constraint. We propose replacing both of these formulations with a conditional value-at-risk (CVaR) formulation, relate RBDO to value-at-risk (VaR), and discuss the tradeoffs among these formulations. Semidefinite Programming and Nash Equilibria in Bimatrix Games Jeffrey Zhang abstract Semidefinite Programming and Nash Equilibria in Bimatrix Games Jeffrey Zhang We explore the power of semidefinite programming (SDP) for finding additive ε-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem and provide a number of valid inequalities to improve the quality of the relaxation. If a rank-1 solution to this SDP is found, then an exact NE can be recovered. We show that for a (generalized) zero-sum game, our SDP is guaranteed to return a rank-1 solution. Furthermore, we prove that if a rank-2 solution to our SDP is found, then a 5/11-NE can be recovered for any game, or a 1/3-NE for a symmetric game. We propose two algorithms based on iterative linearization of smooth nonconvex objective functions which are designed to produce rank-1 solutions. Empirically, we show that these algorithms often recover solutions of rank at most two and ε close to zero. We then show how our SDP approach can address two (NP-hard) problems of economic interest: finding the maximum welfare achievable under any NE, and testing whether there exists a NE where a particular set of strategies is not played. Finally, we show that by using the Lasserre/sum of squares hierarchy, we can get an arbitrarily close spectrahedral outer approximation to the convex hull of Nash equilibria, and that the SDP proposed in this paper dominates the first level of the sum of squares hierarchy. Tame the Flame: Utilizing Methane in Wastewater Treatment Daniel Steinberg abstract Tame the Flame: Utilizing Methane in Wastewater Treatment Daniel Steinberg The Kutztown Wastewater Treatment Plant has posed the question of whether it is worth an investment in new hardware to utilize the methane produced during the digestion of wastewater sludge to supplement the use of fuel oil in heating the digester tank. The Kutztown Wastewater Treatment Plant has indicated that they would like to see a net positive return on their investment within 5 years. In this talk, we present a linear programming model to answer this question. After comparing the heating power of methane to fuel oil, our model showed us how much methane should be stored and how much should be burned over the course of a year. Assuming the price of fuel oil will remain constant at 2016 prices, our 5-year model produced a total savings of approximately \$18,000, without considering the cost of separating and storing the methane. These results tell us how large the budget should be for the addition of the necessary hardware to process and store the methane. Optimization of Inventory for Hip and Knee Joint Operations via Multistage Stochastic Programming Mohammad Pirhooshyaran abstract Optimization of Inventory for Hip and Knee Joint Operations via Multistage Stochastic Programming Mohammad Pirhooshyaran Knee and hip joint replacements are among the most common orthopedic operations. Supplying hospitals with prosthetic implants is difficult because the supply is limited, the demand is stochastic. Often the supply logistics fall to the manufacturer or a distributor. We present a multi-stage stochastic optimization model to optimize the distribution of implants from a central depot to hospitals. We find that our model can reduce costs improve service compared to how our industry partner currently distributes implants. Dimension Reduction for Semidefinite Programming Frank Permenter abstract Dimension Reduction for Semidefinite Programming Frank Permenter We propose a new method for simplifying semidefinite programs (SDP) inspired by symmetry reduction. Specifically, we show if an orthogonal projection satisfies certain invariance conditions, restricting to its range yields an equivalent primal-dual pair over a lower-dimensional symmetric cone---namely, the cone-of-squares of a Jordan subalgebra of symmetric matrices. We then give a simple algorithm for minimizing the rank of this projection and hence the dimension of this cone. Through the theory of Jordan algebras, the proposed method easily extends to linear programming, second-order cone programming, and, more generally, symmetric cone optimization. Energy Storage Network With Charge Level Targets Kursat Kemikli abstract Energy Storage Network With Charge Level Targets Kursat Kemikli We are concerned with the problem of satisfying specified target levels of charge for batteries in a network of batteries and generators subject to random arrivals of demand and energy. The decision variables of the problem involve the scheduling of generators. In this talk, we consider a one-battery problem, discuss multi-battery problems, and compare numerical solution methods for these problems. Forward Sensitivity Analysis for Contracting Stochastic Systems Thomas Flynn abstract Forward Sensitivity Analysis for Contracting Stochastic Systems Thomas Flynn In this talk we discuss our recent work on gradient estimation for contracting stochastic systems. We consider computing derivatives of long-term average costs in these systems using a stochastic variant of forward sensitivity analysis. Differentiability of long-term average (or stationary) costs is established under certain smoothness, integrability, and contraction conditions. To estimate gradients, the system of interest is augmented with a forward sensitivity process constructed from the derivatives of the underlying system. The ergodicity properties of the sensitivity process are analyzed by placing an appropriate Finsler structure on the space, and finding contraction in the corresponding Wasserstein distance. One can get unbiased estimates of the gradient using samples from the stationary distribution of the augmented system. In practice, of course, one can only compute with finite time horizons. Therefore we also consider the rate of convergence of gradient estimates obtained this way. We compare with other approaches to derivative estimation and present some examples, including a stochastic neural network model. Time Varying LPs and SDPs Bachir El Khadir abstract Time Varying LPs and SDPs Bachir El Khadir We study linear semidefinite programs whose data (e.g., the matrices A, b and c in the LP case) are not constant but vary polynomially with time. We show that, under some conditions, we can approximate the optimal value of these problems arbitrarily well by searching for solutions that are polynomial functions of time themselves. Furthermore, we show that the problem of finding the optimal polynomial solution of a given degree can be cast exactly as a semidefinite program. Integrated Modeling of Food-Energy-Water in Ethiopia Sriram Sankaranarayanan abstract Integrated Modeling of Food-Energy-Water in Ethiopia Sriram Sankaranarayanan We present an integrated partial equilibrium model for food and energy markets that computes food production and trade volumes in Ethiopia, and models power generation and transmission from hydel and geothermal power stations. Coupling these models though prices and quantities along their supply chains, we asses shifts in welfare under policy scenarios. We run the model under improved irrigation capabilities, crop rotation strategies, and injection of food aid during crop failure. 15:00 15:15 Coffee break 15:15 16:15 Plenary talk  Aircraft Design via Numerical Optimization: A Multidisciplinary Approach Joaquim R. R. A. Martins abstract Aircraft Design via Numerical Optimization: A Multidisciplinary Approach Joaquim R. R. A. Martins Aircraft are prime examples of engineering systems where several disciplines are interdependent and thus aircraft design requires not only multi-physics simulations, but also multidisciplinary design optimization to achieve optimal trade-offs between the disciplines. One of the main challenges is the aircraft wing flexibility, which requires the consideration of both the aerodynamics and structures disciplines. To address this, the simultaneous optimization of the outer mold line of a wing and its structural sizing is proposed. The solution of such design optimization problems is made possible by a framework for high-fidelity aerostructural optimization. This framework combines a three-dimensional CFD solver, a finite-element structural model of the wing, a geometry modeler, and a gradient-based optimizer. This framework computes the flying shape of a wing and is able to optimize aircraft configurations with respect to hundreds of aerodynamic shape and internal structural sizes. The theoretical developments include coupled-adjoint sensitivity analysis, and an automatic differentiation adjoint approach. The algorithms resulting from these developments are all implemented to take advantage of massively parallel computers. Applications to the optimization of aircraft configurations demonstrate the effectiveness of these approaches in designing aircraft wings for minimum fuel burn. The results show optimal tradeoffs with respect to wing span and sweep, which was previously not possible with high-fidelity single-discipline models. 16:15 16:30 Coffee break 16:30 18:30 Parallel technical sessions  Linear Optimization, Graphs and Networks Conic Optimization Combinatorial Optimization Fourier Optimization for the Box Minorant Problem Robert Vanderbei abstract Fourier Optimization for the Box Minorant Problem Robert Vanderbei There are several important problems at the intersection of Fourier analysis, number theory, and geometry, where infinite dimensional linear programs (with Fourier analytic constraints) play a prominent role. One example is the sphere packing problem in higher dimensions. Another example (the one that we will focus on) is the Beurling-Selberg Box Minorant Problem. We will survey recent results on this topic, especially highlighting the fact that the infinite dimensional linear programs admit novel finite dimensional linear programming bounds. Polynomial Norms and Semidefinite Optimization Georgina Hall abstract Polynomial Norms and Semidefinite Optimization Georgina Hall We establish when the d-th root of a multivariate degree-d polynomial produces a norm. In the quadratic case, it is well-known that this is the case if and only if the matrix associated with the quadratic form is positive definite. We present a generalization of this result to higher order polynomials and show that there is a hierarchy of semidefinite programs that can detect all polynomial norms. A Branch-and-cut Algorithm for Discrete Bilevel Linear Programs Osman Ozaltin abstract A Branch-and-cut Algorithm for Discrete Bilevel Linear Programs Osman Ozaltin We present a branch-and-cut algorithm for solving discrete bilevel linear programs where the upper-level variables are binary and the lower-level variables are either pure integer or pure binary. This algorithm performs local search to find improved bilevel-feasible solutions. We strengthen the relaxed node subproblems in the branch-and-cut search tree by generating cuts to eliminate all of the upper-level integer feasible solutions explored during the local search step. Furthermore, to avoid repeatedly solving similar bilevel integer problems in the local search, we derive structural properties of the value functions of bilevel integer programs. Most notably, we generalize the integer complementary slackness theorem to bilevel integer programs. We also propose three efficient approaches for computing the bilevel programming value functions. Our computational results show that the proposed branch-and-cut approach enhanced with the implementation of value functions and local search can solve discrete bilevel programming instances with up to 200 variables and 150 constraints in a reasonable amount of time. Improved Basic Procedure for Chubanov's Algorithm Carlos Deck abstract Improved Basic Procedure for Chubanov's Algorithm Carlos Deck This work improves Chubanov's projection algorithm for the linear feasibility problem of finding a non-negative vector in Ker(A). This is done by working in the original space of the x-variables instead of solving the alternative system. By changing the solution space, we can focus on solutions within the unit simplex instead of the unit hypercube, which strengthen the cuts provided by Chubanov and Roos. We show how to perform the rescaling in this setting, given that the feasible region is no longer homogeneous. Preliminary computational experiments show an improvement compared to Chubanov and Roos' variants of this algorithm in practice. Warm-start of Interior Point Methods for Second Order Cone Optimization via Rounding over Optimal Jordan Frames Sertalp Cay abstract Warm-start of Interior Point Methods for Second Order Cone Optimization via Rounding over Optimal Jordan Frames Sertalp Cay Interior point methods (IPM) are the most popular approaches to solve Second Order Cone Optimization (SOCO) problems, due to their theoretical polynomial complexity and practical performance. In this paper, we present a warm-start method for primal-dual IPMs to reduce the number of IPM steps needed to solve SOCO problems that appear in a Branch and Conic Cut (BCC) tree when solving Mixed Integer Second Order Cone Optimization (MISOCO) problems. Our method exploits the optimal Jordan frame of a related subproblem and provides a conic feasible primal-dual initial point for the self-dual embedding model by solving two auxiliary linear optimization problems. Numerical results on test problems in the CBLIB library show on average around 61% reduction of the IPM iterations for a variety of MISOCO problems. The Inmate Assignment Problem Anshul Sharma abstract The Inmate Assignment Problem Anshul Sharma In this presentation, we present the inmate assignment problem (IAP), which is the mathematical optimization formulation of the problem each correctional systems face: one has to assign the inmates to available facilities while all legal restrictions and best practice constraints are considered. We develop a Mixed Integer Linear Optimization (MILO) model, which accurately describes the IAP. By presenting a real world case, we also demonstrate that the MILO model can be solved efficiently. The model and methodology can be used for the assignment of inmates in any correctional system. To the best of our knowledge, this is the first time that the IAP is modeled as a mathematical optimization problem. New Extended Formulation for the Steiner Tree Problem Bartosz Filipecki abstract New Extended Formulation for the Steiner Tree Problem Bartosz Filipecki The Steiner tree problem (STP) is one of classical NP-hard combinatorial optimization problems. Given an undirected graph with edge costs, the objective is to find a minimum-cost spanning tree of a subset of vertices called terminals. Possible applications of the STP include network wiring and routing and bioinformatics. Current linear programming algorithms for the Steiner tree problem rely mostly on one of two approaches - the bidirected cut relaxation (BCR) and hypergraphic formulations. These were proven to have an upper bound on the integrality gap of 2 and 1.39 respectively, while the lower bounds based on constructed graph instances are 1.16 and 1.14. We propose a new hierarchy of improving extended formulations for the Steiner tree problem, originating from BCR. We show that our hierarchy achieves a better lower bound on all graph instances used to prove worst case lower bounds for both bidirected cut and hypergraphic formulations. Our approach can be adjusted to solve variants of the STP, for example the Steiner forest problem, or applied to hypergraphic formulation for further potential improvement. Globally solving Non-Convex Quadratic Programs via Linear Integer Programming techniques Wei Xia abstract Globally solving Non-Convex Quadratic Programs via Linear Integer Programming techniques Wei Xia A quadratic program (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This is done via the reformulation of QP as a linear complementary problem, and the use of binary variables together with some fundamental results on the solution of perturbed linear systems, to model the complementary constraints. Reformulating non-convex QPs as MILPs provides an advantageous way to obtain global solutions as it allows to use current state-of-the-art MILP solvers. To illustrate, we compare the performance of our solution approach with the current benchmark global QP solver quadprogBB on a large variety of QP test instances. The MATLAB code, called quadprogIP, and the instances used to perform these numerical experiments are publicly available at https://github.com/xiawei918/quadprogIP. An Algorithm for$P|p_j=p, intree|\sum C_j$Tianyu Wang abstract An Algorithm for$P|p_j=p, intree|\sum C_j$Tianyu Wang We consider the scheduling problem with equal length tasks with in-tree precedence constraints and identical parallel machines, where the objective function is the mean flow time (the sum of completion time). Recently, this problem has been proven NP-complete. However, when the number of machines is a given fixed number, the problem is polynomially solvable. The complexity of the existing algorithm for the problem is$O(n^m)$, where$n$is the number of tasks and$m$is the number of machines. In this talk, we present a new algorithm. The complexity of the algorithm is$O((mh)^m)$, where$h$is the height of the in-tree. This algorithm works better especially when the number of tasks on the same level is large. We show also the experimental result of the algorithm in comparison with the existing one. An Augmenting Flow Algorithm for a Class of Node-capacitated Maximum Flow Problems Rob Curry abstract An Augmenting Flow Algorithm for a Class of Node-capacitated Maximum Flow Problems Rob Curry We consider a class of maximum flow problems having node- and arc-capacity constraints, in which each unit of flow on arc (i,j) consumes a non-negative amount of capacity at node i. Rather than solving a linear program for these problems, we present an augmenting flow algorithm. In this algorithm, we augment flows along a path having positive residual capacities among all arcs and nodes along the path. When no such paths exist, we find and augment flow along flow-cycles that increase the residual capacity at an incapacitated node. We prove the optimality and computational complexity of our algorithm and apply it to solve various problems in wireless sensor network settings. Non-Negative Polynomial Optimization via Moment Conic Optimization Mehdi Ranjbar abstract Non-Negative Polynomial Optimization via Moment Conic Optimization Mehdi Ranjbar We investigate the non-negative univariate polynomial conic optimization problem. It is well-known that the moment cone is the dual of the non-negative polynomial cone. Also, it is known that optimization over the moment cone can be formulated as a semidefinite optimization problem (SDP). However, there are two main drawbacks with the SDP formulation:$1$. The special formulation is extremely ill-conditioned and$2$. It increases the size of the problem by a quadratic factor. For the first issue, we propose to use the Chebyshev polynomial basis. Numerical results show that this basis improves the numerical stability of the interior point method dramatically. For the second issue, we use the so-called non-symmetric interior point (IP) approach. However, since the known self-concordant barrier functions for the non-negative polynomial cone are difficult to work with we apply the non-symmetric IP method to the dual (that is the moment) cone. There are efficient and numerically stable self-concordant barriers for the moment cone. We take advantage of this duality and develop an efficient non-symmetric dual interior point algorithm to solve optimization problems over the non-negative polynomials. We present some numerical results. An Experimental Comparison of Two-dimensional Probabilistic Bin Packing Problem Solution Strategies Sassi Mahfoudh Soumaya abstract An Experimental Comparison of Two-dimensional Probabilistic Bin Packing Problem Solution Strategies Sassi Mahfoudh Soumaya The Probabilistic Bin Packing Problem (PBPP) is a generalization of the classical Bin Packing Problem (BPP) which involves packing a number of rectangular items into the minimum number of identical bins. PBPP is essentially a BPP in which the number of items to be packed is a random variable : on any given instance of the problem, only a subset of items is present. To solve such problem, we consider two strategies : redistribution strategy and priori strategy. The redistribution strategy involves distributing the subset of present items according to a heuristic H. As for the second, we determine a priori packing through all items then via modification methods we erase the absent items from the priori packing and adapt it to the subset of present items. We present in this paper a comparison between the two strategies through numerical experiments. Thus, we aim to find which one generates results near those given by the re-optimization strategy which is impossible to carry out in practice. 19:00 21:00 Graduate Student Social - Packer House, 217 West Packer Avenue, Bethlehem ## Thursday 17th of August 2017 8:00 8:30 Registration and breakfast 8:30 9:30 Plenary talk  Some Recent Interactive Methods for Multiobjective Optimization Kaisa Miettinen abstract Some Recent Interactive Methods for Multiobjective Optimization Kaisa Miettinen Multiobjective optimization is needed because real-life optimization problems typically have several conflicting objective functions. Because of the conflict, we have multiple so-called Pareto optimal solutions where improvement in one objective function is possible only by allowing impairment in at least one of the others. Typically, we need additional preference information from a domain expert, a decision maker, to find the most preferred Pareto optimal solution as the final solution to be implemented. Many methods have been developed for multiobjective optimization problems. In interactive methods, the decision maker takes actively part in the solution process by providing preference information and can learn about the interdependencies among the objective functions. (S)he can also adjust one's preferences while learning and concentrate on solutions that seem most promising. In real applications, function evaluations may be time-consuming and we pay special attention to the dealing with this challenge. We discuss interactive methods NIMBUS, Pareto Navigator, NAUTILUS and NAUTILUS-Navigator. The NIMBUS method has been widely utilized in various application fields and Pareto Navigator has been directed at computationally expensive problems. The NAUTILUS method family questions the widely-used thinking of moving among Pareto optimal solutions during the solution process and starts from the worst possible objective function values and proceed towards the most preferred Pareto optimal solution without the need of trading off. Finally, as the name suggests, NAUTILUS-Navigator hybridizes the two above-mentioned methods and is applicable for computationally expensive problems. 9:30 9:45 Coffee break 9:45 11:15 Parallel technical sessions  Machine Learning Nonlinear Optimization Combinatorial Optimization Optimization Methods for Supervised Learning of Neural Networks Dimitri Papadimitriou abstract Optimization Methods for Supervised Learning of Neural Networks Dimitri Papadimitriou Given a set of labeled data points, the optimization problem associated to the training of neural networks aims at determining the parameters, e.g., synaptic weights, which minimizes the empirical loss between the true output to the given input and the predicted output. The empirical loss minimization problem is nonconvex (even when the loss function is convex), nonsmooth and high-dimensional. We analyze and compare extended bundle and trust region methods for nonconvex loss and non/convex non/smooth regularization term. Phi-Function Technique in Optimization Packing Problems Tatiana Romanova abstract Phi-Function Technique in Optimization Packing Problems Tatiana Romanova In this paper we discuss the main tool of our studies, phi-function technique that we use for analytic description of relations between geometric objects placed in a container taking into account their continuous rotations, translations and distance constraints. We formulate a basic optimization packing problem and introduce its exact mathematical model in the form of a nonlinear continuous programming problem, using phi-functions and quasi-phi-functions. To show the advantages of our tools we apply them to the packing problem of polyhedrons in a container of minimal volume. This problem has a wide spectrum of industrial applications (in modern biology, mineralogy, medicine, materials science, nanotechnology, robotics, space apparatus control systems, mechanical engineering, shipbuilding, aircraft construction, civil engineering). We develop an efficient solution algorithm, which employs a fast starting point algorithm and a new original compaction procedure. The procedure reduces our problem to a sequence of nonlinear programming sub-problems of considerably smaller dimensions and smaller numbers of nonlinear inequalities. Several new computational results for packing polyhedrons (convex and non-convex) in different containers (a cuboid, a cylinder, a ball, an ellipsoid, a convex region that is formed by nonempty intersection of the listed shapes) and comparison with already published instances are provided. We also give some examples for packing 2D&3D objects, including ellipses and ellipsoids. Point Cover Problem in 3D Sharmin Akter abstract Point Cover Problem in 3D Sharmin Akter We examine the problem of covering points with minimum number of axis-parallel lines in 3-dimensional space which is an NP-complete problem. We study the lift-and-project relaxation of the standard integer program to obtain a lower bound. This method is used to strengthen the integrality gap of a problem. We explore the lagrangian relaxation with subgradient optimisation technique and our experimental results show that it gives very good lower bounds at reasonable computational cost. We present a hybrid method in which we solve the lift-and-project LP using subgradient optimisation procedure. We propose an approximation algorithm which iteratively uses the lagrangian relaxation method. We also study a branch and bound method which gives the optimal integral solution. Finally, we observe that the empirical approximation ratio of the point cover problem in 3-dimensional space is at most 3/2 based on the experimental evaluation. - This is a joint work with Daya Ram Gaur. The Possibility of Doing Sparse Coding by Deep Nets Anirbit Mukherjee abstract The Possibility of Doing Sparse Coding by Deep Nets Anirbit Mukherjee In "Dictionary Learning" one is trying to recover incoherent matrices$A^* \in R^{n \times h}$(typically overcomplete and whose columns are assumed to be normalized) and sparse vectors$x^* \in R^h$with a small support while being given access to observations$y \in R^n$where$y = A^*x^*$. In this work we undertake a rigorous analysis of the possibility that dictionary learning could be performed by gradient descent on "Autoencoders" which are the$R^n \to R^n$neural network with a single ReLU activation layer of size$h$. Towards the above objective we propose a new autoencoder loss function which modifies the squared loss error term and also adds new regularization terms. Then we undertake an explicit analysis of the expected gradient of this loss function and analyze the stationary points of it which are assumed to be within a small constant distance from the original dictionary. We make stochastic assumptions about the sampling and assume upperbounds on how the support size and the magnitudes of the non-zero entries of the test sparse vectors are increasing with the sparse code dimension. We also put in corresponding upperbounds on how fast the incoherence of$A^*$is decreasing with$h$. Then in the limit of large enough sparse code dimension we are able to show that from these stationary points of our loss function one can recover a dictionary whose action on the sparse vectors is indistinguishable from that of$A^*$. Condition Numbers for Convex Functions with Polytope Domains David Gutman abstract Condition Numbers for Convex Functions with Polytope Domains David Gutman In this talk we propose new condition numbers for convex functions with polytope domains. These condition numbers naturally arise in the convergence analysis of Frank-Wolfe (FW) algorithm variants for optimizing a convex function over a polytope. Among the discussed variants are three new accelerated FW type algorithms that we propose. These new condition numbers enable us to prove that each proposed accelerated variant improves upon the theoretical convergence rates of the common FW variants. A Novel Approach to Model and Solve Discrete Truss Sizing Problems Mohammad Shahabsafa abstract A Novel Approach to Model and Solve Discrete Truss Sizing Problems Mohammad Shahabsafa In this paper, we consider various mathematical models for the truss topology design problem (TTDP) with the objective to minimize the truss weight. The non-convex Euler buckling constraints and Hooke's law are also considered. We deal with the truss design problems where the cross sectional areas of the bars take only discrete values. We propose novel Mixed Integer Linear Optimization Model (MILO) reformulations of the non-convex models. The resulting MILO models are not solvable with existing MILO software. We propose a novel solution methodology to solve the MILO models, and present numerical experiments to demonstrate the power of the novel computational methodology. SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient Martin Takac abstract SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient Martin Takac In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic methods such as SVRG, S2GD, SAG and SAGA, SARAH admits a simple recursive framework for updating stochastic gradient estimates; when comparing to SAG/SAGA, SARAH does not require a storage of past gradients. The linear convergence rate of SARAH is proven under strong convexity assumption. We also prove a linear convergence rate (in the strongly convex case) for an inner loop of SARAH, the property that SVRG does not possess. Numerical experiments demonstrate the efficiency of our algorithm. Symmetric Factorization of Saddle-point Matrices in Nonlinear Optimization and Reusing Pivots Jan Kuratko abstract Symmetric Factorization of Saddle-point Matrices in Nonlinear Optimization and Reusing Pivots Jan Kuratko Iterative methods for nonlinear optimization usually solve a sequence of linear systems. In this talk we will address the application of direct methods in solving linear systems where the matrix is symmetric and indefinite. Moreover, we assume that the matrices from that sequence of linear systems are related such that the structure of blocks and bands of nonzero elements remains the same. We solve the linear system by the symmetric indefinite factorization that is by Bunch-Parlett or Bunch-Kaufman methods. We will describe how to use the knowledge of the pattern of 1x1 and 2x2 pivots from one iteration in the next iteration of the optimization method. We will describe our strategy for monitoring the pivots and the stability of the factorization. According to our strategy we either skip searching for pivots or update the permutation matrix if needed. In addition, we will present our method that adaptively switches from the signed Cholesky factorization to Bunch-Parlett or Bunch-Kaufman. We will show on examples that this monitoring strategy reduces the time spent on searching the matrix for pivots. Column Generation Approach to the Convex Recoloring Problem on a Tree Sangho Shim abstract Column Generation Approach to the Convex Recoloring Problem on a Tree Sangho Shim The convex recoloring (CR) problem is to recolor the nodes of a colored graph at minimum number of color changes such that each color induces a connected subgraph. We adjust to the convex recoloring problem the column generation framework developed by Johnson, Mehrotra and Nemhauser (Mathematical Programming 62 (1993) 133-151). For the convex recoloring problem on a tree, the subproblem to generate columns can be solved in polynomial time by a dynamic programming algorithm introduced by Chopra et al. (Mathematical Programming First Online (July 13, 2016) doi:10.1007/s10107-016-1050-2). Given a large number of colors, the column generation framework performs much better than the integer programming model introduced by Chopra et al. 11:15 11:30 Coffee break 11:30 12:30 Mopta Modeling Competition  Mopta Modeling Competition Peter Nieuwesteeg abstract Mopta Modeling Competition Peter Nieuwesteeg The ninth AIMMS/MOPTA Optimization Modeling Competition is a result of cooperation between AIMMS and the organizers of the MOPTA conference. Teams of three graduate students participated and solved a a scheduling problem. The teams had to form a mathematical model of the problem, implement it in AIMMS, solve it, create a graphical user interface, and write a 15-page report on the project. The panel of judges selected two teams for the final. Alphabetically: apIO (Colombia) and The Duo Solution (Netherlands). 12:30 13:30 Lunch 13:30 15:00 Parallel technical sessions  Machine Learning Nonlinear Optimization Data Driven and Real Time Optimization Hyperparameter Tuning Using Model-based Derivative-free Optimization Katya Scheinberg abstract Hyperparameter Tuning Using Model-based Derivative-free Optimization Katya Scheinberg We will discuss several black-box optimization applications that arise in machine learning and will show how they can be solved by model-based derivative free trust-region method. We will also discuss a stochastic version of the method and its application to machine learning. Complexity Analysis of Second-order Line Search Algorithms for Smooth Non-convex Optimization Clément Royer abstract Complexity Analysis of Second-order Line Search Algorithms for Smooth Non-convex Optimization Clément Royer There has recently been a growth of interest in algorithms dedicated to solving unconstrained smooth nonconvex optimization problems, partly due to the outbreak of such instances in neural networks and robust statistics. For these schemes, the derivation of complexity guarantees has become an increasingly popular area of research. In particular, second-order Newton-type methods such as regularization and trust-region techniques have been analyzed from such a perspective. More recent proposals, essentially based on first-order aspects, have also been shown to enjoy optimal iteration complexity rates, while providing additional guarantees concerning the computational cost of the associated method. In this talk, we present a line-search algorithm that shares similar features with the aforementioned frameworks. A key property of the method is its ability to choose between different steps, such as gradient and Newton ones, in order to produce a sufficient decrease in the function value: this process is driven by the amount of nonconvexity detected at the current iterate. We show that the resulting framework enjoys favorable iteration complexity and convergence rates. We then introduce inexactness in the direction computation, thereby leveraging iterative linear algebra procedures, of deterministic and randomized types. Such techniques have a direct impact on our complexity results, as those reflect the additional expense induced by inexact properties. Developing a Nonlinear Predictor for an Unmeasured Signal Based on Integral Data Andrew Stamps abstract Developing a Nonlinear Predictor for an Unmeasured Signal Based on Integral Data Andrew Stamps A frequent challenge in the control and optimization of chemical processes is the lack of (reliable) measurements for critical quantities of interest. It is therefore necessary to develop a model to predict the unmeasured quantity using available signals. This work considers the case where one liquid inlet/outlet flow of a tank is unknown while the tank level, all other flows, and corresponding control valve positions are known. Given that tank inventory is the integral of net flow into the tank, a regression problem is formulated to determine the unknown flow as the integrand of level depending on one or more process variables, such as valve positions. In general, the relationship between flow and control valve position is nonlinear without a well-defined functional form. Therefore, cubic splines are chosen for their simplicity and flexibility. Moreover, constraints that arise from the physical understanding of the system, such as monotonicity and concavity, can be enforced in a straightforward manner with linear constraints on the fitting parameters. While cubic spline regression has received much attention in the literature over the years, this work is a non-traditional application of the technique. Using this framework, an example is presented where a complex nonlinear model of a cryogenic liquid flow is regressed as a function of three process variables over months of curated operating data. The results are shown to be accurate within about 2% over a wide range of operating conditions. Predictors of this sort have applications in both the development and implementation of real-time process optimizations, providing nonlinear transforms to simplify subsequent regression models as well as tools to compute the initial state of the system each time the optimization is run. Wasserstein Distributional Robustness and Regularization in Statistical Learning Rui Gao abstract Wasserstein Distributional Robustness and Regularization in Statistical Learning Rui Gao A central problem in statistical learning is to design algorithms that not only perform well on training data, but also generalize to new and unseen data. In this paper, we tackle this problem by formulating a distributionally robust stochastic optimization problem, which minimizes the worst-case expected loss over a family of distributions that are close to the empirical distribution in Wasserstein distances. We establish a relation between such Wasserstein distributionally robust stochastic optimization and gradient-norm regularization. In particular, we identify a broad class of loss functions, for which the worst-case expected loss is upper and lower bounded by some gradient-norm regularization problems. Moreover, we show that the gap between the upper and lower bounds is asymptotically zero with probability one. The relation between Wasserstein distributional robustness and regularization has the following important implications: (i) It provides new interpretations for problems involving regularization, including a great number of statistical learning problems, and several discrete choice models such as the multinomial logit. (ii) It enables a new method to derive generalization error bounds for statistical learning problems, by leveraging tools from distributionally robust optimization. For example, we derive an optimal generalization error bound for linear prediction with Lipschitz loss. (iii) It suggests a novel and systematic way to regularize hard problems in deep learning. As an example, we demonstrate superior performance on training generative adversarial networks (GANs) using our new regularization scheme. Communication-Efficient Algorithms for Decentralized and Stochastic Optimization Yi Zhou abstract Communication-Efficient Algorithms for Decentralized and Stochastic Optimization Yi Zhou We consider the class of nonsmooth and stochastic optimization problems defined over multi-agent networks where communication is a major bottleneck. Our major contribution is to present a new class of stochastic decentralized primal-dual type algorithms, namely the stochastic decentralized communication sliding (SDCS) methods, which can skip the inter-node communications while agents solve the primal subproblems iteratively through linearizations of their local objective functions. In comparison with existing results for decentralized nonsmooth and stochastic optimization, we can reduce the total number of inter-node communication rounds by orders of magnitude while still maintaining the optimal complexity bounds on intra-node stochastic subgradient evaluations. Optimization for Data Reconciliation in Large Gas Pipeline Networks Joshua Isom abstract Optimization for Data Reconciliation in Large Gas Pipeline Networks Joshua Isom Gas pipeline networks have tremendous economic importance worldwide. As of September 2016, there were more than 2,700,000 km of natural gas pipelines and more than 4,500 km of hydrogen pipelines worldwide. In the United States in 2015, natural gas delivered by pipeline networks accounted for 29% of total primary energy consumption in the country. In order that the operations of gas pipeline networks can be monitored and controlled, gas pipeline networks are equipped with sensors for measuring gas pressures and flows at various points in the network. By their nature, these measurements are noisy and incomplete. To obtain a full understanding of the operating state of the network, data reconciliation methods are used to obtain a full estimate of the state of the network. Several optimization methods for data reconciliation in gas pipeline networks are compared and contrasted. First, convex optimization methods can provide stable and reliable data reconciliation results, although approximation of the nonlinear physics of the network is required in the formulation of the convex problem. Second, recursive Kalman filters can provide a higher degree of accuracy through the explicit use of a nonlinear physics-based models, at the potential expense of robustness and scalability. Finally, noncovex programming methods may be used to achieve a high-fidelity data reconciliation result, at the potential expense of computation time and repeatability. Use of the three data reconciliation methods is illustrated through application to simulated gas pipeline networks. Hyper-parameter Optimization for Support Vector Machine as a Bilevel Problem Wei Jiang abstract Hyper-parameter Optimization for Support Vector Machine as a Bilevel Problem Wei Jiang Machine learning models usually contain hyper-parameters that need to be optimized to prevent overfitting and minimize generalization error on unseen test data. Currently, the standard approach for assessing the generalization error of machine learning model is cross-validation. The common practice to optimize the hyper-parameters is using grid-search combined with cross-validation for which we search through a range of values for the hyper-parameters and choose the one that yields the best model performance evaluated by cross-validation. This is computational expensive especially given high-dimensional hyper-parameter space. Moreover, local optimal solution is not even guaranteed. We optimize the hyper-parameter (both the regularization and Gaussian kernel parameters) for support vector machine as a bilevel optimization problem by forming it as a single non-convex nonlinear optimization problem using slater's condition and strong duality. We explore different approaches to solve this problem and present the empirical results on few data sets. Accelerating Gradient Descent through Quadratic Lower Bounds Majid Jahani abstract Accelerating Gradient Descent through Quadratic Lower Bounds Majid Jahani In this work, we introduce the concept of an Underestimate Sequence (UES), which is a sequence of lower bounds of the objective function and is a natural extension of Nesterov’s estimate sequence. Moreover, we propose a first order method for minimizing smooth strongly convex functions. The algorithms, based on updating the lower bounds of objective functions, have natural stopping criteria when reach optimality. We show that the accelerated version of our algorithm enjoys the optimal linear rate of convergence on the gap between objective values and minimal values of the lower bounds. Data Management for Model Development at Air Products Suyash Singh abstract Data Management for Model Development at Air Products Suyash Singh Air Products is the world’s leading provider of hydrogen – it owns and operates Steam Methane Reforming plants that produce over 3 billion SCFD of hydrogen, and has over 1500 years of operating experience with these plants. This long history of designing, operating, and maintaining hydrogen plants provides us access to a rich dataset comprising of plant design parameters, real time process data, and a detailed historical account of the outages and failures at each of these facilities. In this work, we use the aforementioned data to study the effect of numerous categorical variables (e.g. plant age, capacity, number of reformer tubes etc.), and process variables (steam to carbon ratio, reformer outlet temperature, plant rates etc.) on the probability of a given plant having an unplanned outage. Statistical methods like partial least squares regression and decision tree learning, among others, were employed to develop a generic model that (a) predicts the probability of a given plant having an outage in the near future, and (b) offers insights into the effect of varying key process variables on the probability of having an outage. Further, we will discuss the incorporation and utilization of these models in the real time control, optimization, and monitoring of Air Products’ assets. 15:00 15:15 Coffee break 15:15 16:15 Plenary talk  The ALAMO Approach to Machine Learning: Best Subset Selection, Adaptive Sampling, and Constrained Regression Nikolaos V. Sahinidis abstract The ALAMO Approach to Machine Learning: Best Subset Selection, Adaptive Sampling, and Constrained Regression Nikolaos V. Sahinidis A central problem in modern computational science is that of learning an algebraic model from data obtained from simulations or experiments. We present a methodology that is designed to use a small number of data points to learn models that are as accurate and as simple as possible. The approach can • construct an algebraic model for a simulation or experimental black-box system • use previously collected data for model building and validation • call a user-specified (simulation/experimental) function to collect additional measurements if needed/desired • enforce response variable bounds, physical limits, and boundary conditions. The proposed methodology has been implemented in the ALAMO software for Automated Learning of Algebraic MOdels. We present extensive computational results with ALAMO and comparisons between ALAMO and a variety of machine learning techniques, including Latin hypercube sampling, simple least-squares regression, and the lasso. Throughout the talk, we provide illustrative examples and describe a number of applications that have been facilitated by ALAMO.e 16:15 16:30 Coffee break 16:30 18:00 Parallel technical sessions  Modeling and Optimizing Energy Systems Conic Optimization OR Applications at the University Parallel Computing of Stochastic Programs with Application to Energy System Capacity Expansion Andrew Liu abstract Parallel Computing of Stochastic Programs with Application to Energy System Capacity Expansion Andrew Liu Power grids’ planning and operations exhibit extreme multiscale, ranging from hourly operation to decades of planning. The linkage of such decisions can be treated in a primal-dual fashion to produce multiple independent subproblems. We propose to use a primal-dual-based proximal method to design a parallel algorithm to solve such multiscale problems. Convergence can be shown for both convex and non-convex problems (in the non-convex case, convergence is understood to a stationary point). We use the algorithm to demonstrate the importance to consider ramping constraints in finer time-scale in long-term capacity planning with large-scale renewable resources. Bad Semidefinite Programs, Now with Short Proofs Gabor Pataki abstract Bad Semidefinite Programs, Now with Short Proofs Gabor Pataki Bad semidefinite programs: now with short proofs Semidefinite programs (SDPs) often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. The main result of our recent paper (“Bad semidefinite programs: they all look the same”, published in SIOPT in 2017) was motivated by the curious similarity of the pathological SDPs in the literature. This paper characterized pathological semidefinite {\em systems} by certain {\em excluded matrices}, which are easy to spot in all published instances. As a byproduct, it showed how to transform semidefinite systems into a canonical form to easily verify their pathological nature. The transformation is surprisingly simple, as it relies mostly on elementary row operations inherited from Gaussian elimination. The proofs in that paper were somewhat involved. In this work we give a very short proof of the main result. The current proof relies mostly on elementary linear algebra, and uses a separation argument from convex analysis just once. Predicting Student Success: Applying the Jaya Algorithm to a Prediction Model Mason Smith abstract Predicting Student Success: Applying the Jaya Algorithm to a Prediction Model Mason Smith In order to improve academic success and retention of students at Kutztown University, we wish to identify those students that are likely to struggle academically, i.e., have a first-semester GPA below 2.0, and provide them with tools for success. To this end, we will present a model to predict the probability that an individual student will have a GPA below 2.0 in their first semester at Kutztown University. Our model incorporates high school GPA, SAT scores, ALEKS Mathematics Placement Assessment scores, and other relevant data. In particular, we implemented the Jaya optimization algorithm due to Rao to determine the coefficients of this model that maximized the correlation between the student data and first semester GPA. Optimal Price-threshold Control for Battery Operation with Aging Phenomenon: A Quasiconvex Optimization Approach Yuhai Hu abstract Optimal Price-threshold Control for Battery Operation with Aging Phenomenon: A Quasiconvex Optimization Approach Yuhai Hu This talk is concerned with grid-level battery storage operations, taking battery aging into consideration. Battery operations under price uncertainty are modeled as a Markov Decision Process with expected cumulated discounted rewards. The structure of the optimal policy is studied. An algorithm that takes advantage of the problem structure and works directly on the continuous state space is developed to maximize the objective over the life of the battery. Computational results are presented to compare the proposed approach to a standard dynamic programming method, and to evaluate the impact of refinements in the battery model. On the Identification of the Optimal Partition for Semidefinite Optimization Ali Mohammad-Nezhad abstract On the Identification of the Optimal Partition for Semidefinite Optimization Ali Mohammad-Nezhad The concept of the optimal partition was originally introduced for linear optimization and linear complementarity problems and subsequently extended to semidefinite optimization. For linear optimization and sufficient linear complementarity problems, the optimal partition and a maximally complementary optimal solution can be identified in strongly polynomial time. In this paper, under no assumption on strict complementarity, we consider the identification of the optimal partition of semidefinite optimization for solutions on, or in a neighborhood of the central path. In contrast to linear optimization and linear complementarity problem, the optimal partition for semidefinite optimization cannot be identified exactly from an interior solution. Instead, we identify the sets of eigenvectors converging to an orthonormal bases for the optimal partition using the bounds for the magnitude of the eigenvalues. The magnitude of the eigenvalues of an interior solution is quantified using a condition number and an upper bound for the distance of an interior solution to the optimal set. We provide iteration complexity bound for the identification of the above sets of eigenvectors An Undergraduate uses OR to Improve Final Exam Schedules at her university Francis Vasko abstract An Undergraduate uses OR to Improve Final Exam Schedules at her university Francis Vasko Final examination scheduling is typically a complex problem that impacts students, faculty, and administrators at every university. In this talk, we describe how an undergraduate student, for her senior project at Kutztown University, analyzed the final exam schedules at Kutztown University to see if she could improve them. Specifically, she wanted to see if she could reduce student conflicts defined to be a student having three exams scheduled on the same day. The approach that she developed, based on a balanced bin packing algorithm, was very appealing because it could be implemented manually by a staff member of the Registrar’s office, requiring at most 30 minutes to generate the schedule. Testing this approach using actual data from the Fall 2015 semester resulted in a 42% reduction in student conflicts. This approach, because of its simplicity and intuitive appeal, was widely accepted by the Kutztown University faculty and administrators and was implemented starting with the Fall 2016 semester. On the Price Impact of Distributed Energy Storage Boris Defourny abstract On the Price Impact of Distributed Energy Storage Boris Defourny This talk is concerned with the price impact of energy storage on electricity prices. A Markov game approach is adopted to model energy storage operations from the supply side and the demand side, aimed at favorably impacting electricity prices. Various repartitions of energy storage capacity ownership are considered. A Simple Preprocessing Algorithm for Semidefinite Programming Yuzixuan Zhu abstract A Simple Preprocessing Algorithm for Semidefinite Programming Yuzixuan Zhu We present a simple preprocessing algorithm for semidefinite programming to reduce the size of the problems, and computational results. 18:00 19:00 Cocktail Reception 19:00 21:00 Banquet ## Friday 18th of August 2017 8:00 8:30 Registration and breakfast 8:30 9:30 Plenary talk  Control and Optimization of Energy Systems Pascal Van Hentenryck abstract Control and Optimization of Energy Systems Pascal Van Hentenryck Building a sustainable energy systems is one of the greatest challenges of our times. It is also a unique opportunity thanks to the emergence of renewable energy technologies, power electronics, battery developments. This talk describes the tremendous progress realized in the last decades in controlling and optimizing energy systems. In particular, we will review the remaining challenges in steady-state optimization and the recent progress in bridging the gap between steady-state optimization and control of energy systems. Extensive computational results will highlight the opportunities and research challenges at the intersection of control and optimization. 9:30 9:45 Coffee break 9:45 11:15 Parallel technical sessions  Modeling and Optimization in Engineering Advances in Large-scale Optimization Stochastic Optimization Piecewise Linearization in a MILP Model: A Case Study Giorgio Fasano abstract Piecewise Linearization in a MILP Model: A Case Study Giorgio Fasano This work is related to a challenging optimal control (OC) problem in space engineering. Our study focuses on the piecewise linearization of non-convex univariate functions used to obtain Mixed Integer Linear Programming (MILP) formulations, in order to approximate the nonlinear OC model. Several linearization techniques, generally involving additional variables and constraints, are available. A well-known approach is based on Special Ordered Sets of type 2 (SOS2) that allows the handling of piecewise linearization algorithmically within a branch-and-bound procedure. The classical approach based on convex combinations, as well as a highly efficient formulation recently introduced by Vielma and Nemhauser, are also reviewed. Here we propose an ad hoc linearization to deal with our OC problem characterized by a special structure involving a large number of univariate functions, each with a rather limited number of breakpoints. The structure of our OC problem makes the proposed linearization approach well-suited. We report experimental results, and discuss extension potentials for the case of approximating multivariate functions. Searching The Growth Rate: Adaptive Svrg Methods Under Error Bound Conditions Qihang Lin abstract Searching The Growth Rate: Adaptive Svrg Methods Under Error Bound Conditions Qihang Lin Error bound condition (EBC), an intrinsic property of an optimization problem, can be exploited for developing algorithms with surprisingly fast global convergence. However, many existing approaches utilizing EBC requires knowing a growth parameter in the statement of EBC, which is usually very difficult to estimate, leading to a gap between the theoretical convergence and practical implementation. To address this issue, we propose a variance reduced stochastic gradient method that automatically searches for this unknown parameter on the fly of optimization, while still maintaining almost the same convergence rate just as the parameter is known. Comparison of Stochastic Service Model and Guaranteed Service Model in Serial System Yinan Liu abstract Comparison of Stochastic Service Model and Guaranteed Service Model in Serial System Yinan Liu The Stochastic Service Model (SSM) and Guaranteed Service Model (GSM) are two competing models for optimizing inventory levels in multi-echelon inventory systems. SSM accounts for the uncertainty in lead times due to upstream stockouts, while GSM treats lead times as bounded deterministically, which is justified by making the relatively strong assumption that the demand is also bounded. SSM models are more representative of real-world supply chains, but GSM models are much more tractable and are therefore widely used in practice. Our research addresses the question of whether GSM models are an effective heuristic for SSM systems. We perform extensive numerical experiments to address this question. Our results suggest that SSM and GSM models agree closely under many conditions, justifying the use of GSM as a heuristic for SSM. On the other hand, the two models diverge significantly for some settings, for example, when the service level is relatively low. Solutions of Minimum-time Velocity Planning Problems Mattia Laurini abstract Solutions of Minimum-time Velocity Planning Problems Mattia Laurini For a vehicle on an assigned path, we find the time-optimal speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We present a necessary and sufficient condition for the feasibility of the problem and a simple operator, based on the solution of two ordinary differential equations, which computes the optimal solution. Theoretically, we show that the problem feasible set, if not empty, is a lattice, whose supremum element corresponds to the optimal solution. Moreover, after the addition of “comfort” constraints imposed over the acceleration’s derivative, we are able to solve the resulting problem with an arbitrarily high precision by performing a finite element lengthwise path discretization and using a quadric spline for interpolation. In particular, we show that an ε-optimal solution can be found in a time which is a polynomial function of ε−1. Asynchronous Parallel Primal-dual Coordinate Update Method Yangyang Xu abstract Asynchronous Parallel Primal-dual Coordinate Update Method Yangyang Xu Recent several years have witnessed the surge of asynchronous (async-) parallel computing methods due to the extremely big data involved in many modern applications and also the advancement of multi-core machines and computer clusters. In optimization, most works about async-parallel methods are on unconstrained problems or those with block separable constraints. In this talk, I will present an async-parallel method based on block coordinate update (BCU) for solving convex problems with nonseparable linear constraint. Running on a single node, the method becomes a novel randomized primal-dual BCU with adaptive stepsize for multi-block affinely constrained problems. For these problems, Gauss-Seidel cyclic primal-dual BCU needs strong convexity to have convergence. Merely assuming convexity, I will show that the objective value sequence generated by the new algorithm converges in probability to the optimal value and also the constraint residual to zero. Numerical experiments will also been shown to demonstrate the efficiency of the proposed method and significantly better speed-up performance than its sync-parallel counterpart. Chance Constrained Optimal Power Flow with Non-Affine Control Policies Yury Dvorkin abstract Chance Constrained Optimal Power Flow with Non-Affine Control Policies Yury Dvorkin Chance constrained programming is a computationally affordable approach to manage operational uncertainties in power systems with significant penetration levels of renewable generation. Previous studies have demonstrated that under the assumption of affine control policies and normally distributed uncertainties, chance constrained optimal power flow formulations can be converted into second-order cone programs. This presentation will demonstrate the effect of using non-affine control policies and other than normally distributed uncertainties in such formulations. Specifically, this presentation will touch on modeling so-called primary frequency response constraints with a non-affine speed-droop governor characteristic using a chance constrained framework. The presentation will also discuss some computational results obtained on a modification of the 118-bus IEEE Reliability Test System. Nonlinear Regression Analysis by Global Optimization: A Case Study in Space Engineering Janos D. Pinter abstract Nonlinear Regression Analysis by Global Optimization: A Case Study in Space Engineering Janos D. Pinter The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically. The limitations of such approaches in the nonlinear context are well known. In order to properly address this issue, global optimization strategies can be used to find ((numerically)) the best possible model parameterization. This work discusses an application of nonlinear regression model development and calibration in the context of space engineering. We study a scientific instrument, installed on-board of the International Space Station and aimed at studying the Sun’s effect on the Earth’s atmosphere. A complex sensor temperature monitoring objective has motivated the adoption of an ad hoc calibration methodology. Due to the non-convexity of the underlying regression model, a global optimization approach has been implemented. The LGO software package is used to carry out the numerical optimization required periodically for each stage of the analysis. We report computational performance results and offer related insight. Our case study shows the robust and efficient performance of the global scope model calibration approach. Gradient Sliding Framework for Convex Composite Optimization Yuyuan Ouyang abstract Gradient Sliding Framework for Convex Composite Optimization Yuyuan Ouyang We show that one can skip gradient computations for gradient descent type methods applied to convex composite optimization problems with certain structure. Examples of useful special structures include sum of two smooth functions, saddle-point reformulation for regularization terms, variational inequalities reformulation of the objective function, and also linear constraints. In particular, we prove that one only needs${\cal O}(1/\sqrt{\epsilon})$gradient computations for the smooth component while still preserving the overall iteration complexity for solving these structured problems Acceptable Risks and Related Decision Problems with Multiple Risk-averse Agents Getachew Befekadu abstract Acceptable Risks and Related Decision Problems with Multiple Risk-averse Agents Getachew Befekadu In this talk, we consider a risk-averse decision problem for systems governed by controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents make their decisions in such a way to minimize their individual accumulated risk-costs over a finite-time horizon. In particular, we introduce multi-structure dynamic risk measures induced from conditional$g\$-expectations, where the latter are associated with the generator functionals of certain BSDEs that take into account the risk-cost functionals of the agents. Here, we also assume that the solutions for such BSDEs {\it almost surely} satisfy a stochastic viability property w.r.t. a certain given closed convex set. Moreover, using a result similar to that of the Arrow-Barankin-Blackwell theorem, we establish the existence of consistent optimal decisions for the risk-averse agents, when the set of all Pareto optimal solutions, in the sense of viscosity, for the associated dynamic programming equations is dense in the given closed convex set. Finally, we briefly comment on the characteristics of acceptable risks vis-\'{a}-vis some uncertain future costs or outcomes, where results from the dynamic risk analysis constitute part of the information used in the risk-averse decision criteria.
11:15 11:30 Coffee break
11:30 12:30 Plenary talk
 Unified Treatment of First-order Methods Stephen Vavasis abstract Unified Treatment of First-order Methods Stephen Vavasis We consider three first-order methods for smooth, strongly convex optimization, namely, accelerated gradient, geometric descent, and, for the special case of quadratics, linear conjugate gradient. We establish several relationships among these methods including: all three can be regarded as realizations of an "idealized algorithm", all three decrease the same computable potential at the same rate, and all three can be analyzed using Bubeck, Lee and Singh's ellipsoid idea. Some consequences of the unified treatment are as follows. First, we obtain a new proof (with a slightly worse constant, but more constructive) of Daniel's classic bound on the convergence rate of conjugate gradient. Second, the unified treatment points the way to new hybrid methods that act like nonlinear conjugate gradient but with better guarantees. Third, we can get new insight into inexact linear conjugate gradient. Finally, we look at problems beyond smooth, strongly convex optimization. This presentation represents joint work with S. Karimi.
12:30 13:30 Lunch