Research

My research interests are mainly in the area of Mathematical Programming. See also my publication webpage.

Mixed-Integer Nonlinear Programming (MINLP)

MINLP problems are of the form

\begin{array}{rll}\min & f_0(x,y) \\ & f_i (x,y) \le 0 & \forall i=1,2\ldots,m\\ & x\in \mathbb R^n, y\in \mathbb Z^p\end{array}

where allf_i(x,y)are, in general, nonlinear functions. The above problem is representative of a large class of Optimization problems. See more…

Multicommodity Network flow

Shared protection constraints, step-wise node cost functions, uncertainty in the traffic demand, OSPF routing, multi-layer structure. Bundle methods, Column generation, Cutting planes, Second-order Cone programming, and Branch&Price algorithms. See more…

Relaxation methods…

… and their applications to large, infeasible systems of linear inequalities. See also MaxFS, a web page for the dissemination of MaxFS, an important problem in Optimization. My contributions to the area include an algorithm that implements a randomized, thermal version of the relaxation method. See more…

Presentations

  • IMA Hot Topics in Mixed Integer Nonlinear Programming (video, slides).