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info:tech_report_example.tex [1998/12/03 12:11] |
info:tech_report_example.tex [2016/03/16 13:19] aykutbulut |
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+ | < | ||
+ | \def\coralreport{1} | ||
+ | %\documentclass{./ | ||
+ | \documentclass{article} | ||
+ | \usepackage{ifthen} | ||
+ | %\usepackage{float} | ||
+ | \usepackage{complexity} | ||
+ | \usepackage{algorithm} % for algorithm environment | ||
+ | \usepackage{algpseudocode} % for algorithmic environment | ||
+ | | ||
+ | | ||
+ | \usepackage{amsmath} | ||
+ | \usepackage{amssymb} | ||
+ | \usepackage{graphicx} | ||
+ | \usepackage[authoryear]{natbib} | ||
+ | |||
+ | % for tiles and keywords | ||
+ | \usepackage{authblk} | ||
+ | \usepackage{geometry} | ||
+ | \usepackage{fullpage} | ||
+ | \newtheorem{theorem}{Theorem} | ||
+ | \newtheorem{claim}{Claim} | ||
+ | \newtheorem{definition}{Definition} | ||
+ | |||
+ | |||
+ | \renewcommand{\Re}{\mathbb{R}} | ||
+ | \algdef{SE}[DOWHILE]{Do}{doWhile}{\algorithmicdo}[1]{\algorithmicwhile\ #1} | ||
+ | % todo(aykut) this will create a problem with \P command of complexity package. | ||
+ | \renewcommand{\P}{\mathcal{P}} | ||
+ | |||
+ | \setlength{\evensidemargin}{0in} | ||
+ | \setlength{\oddsidemargin}{0in} | ||
+ | \setlength{\parindent}{0in} | ||
+ | \setlength{\parskip}{0.06in} | ||
+ | |||
+ | |||
+ | \ifthenelse{\coralreport = 1}{ | ||
+ | \usepackage{isetechreport} | ||
+ | \def\reportyear{15T} | ||
+ | % The report number is the same one used in the ISE tech report series | ||
+ | \def\reportno{001} | ||
+ | % This is the revision number (increment for each revision) | ||
+ | \def\revisionno{0} | ||
+ | % This is the date f the original report | ||
+ | \def\originaldate{March 13, 2015} | ||
+ | % This is the date of the latest revision | ||
+ | \def\revisiondate{March 13, 2015} | ||
+ | % Set these variables according to whether this should be a CORAL or CVCR | ||
+ | % report | ||
+ | \coralfalse | ||
+ | \cvcrfalse | ||
+ | \isetrue | ||
+ | |||
+ | }{} | ||
+ | |||
+ | \begin{document} | ||
+ | |||
+ | \title{On the Complexity of Inverse MILP} | ||
+ | |||
+ | \ifthenelse{\coralreport = 1}{ | ||
+ | \author{Aykut Bulut\thanks{E-mail: | ||
+ | \author{Ted K. Ralphs\thanks{E-mail: | ||
+ | \affil{Department of Industrial and Systems Engineering, | ||
+ | \titlepage | ||
+ | }{ | ||
+ | \author{Aykut Bulut} | ||
+ | \author{Ted K. Ralphs} | ||
+ | \affil{COR@L Lab, Department of Industrial and Systems Engineering, | ||
+ | \date{\today} | ||
+ | } | ||
+ | |||
+ | \maketitle | ||
+ | |||
+ | \begin{abstract} | ||
+ | Inverse optimization problems determine problem parameters that are closest to | ||
+ | the estimates and will make a given solution optimum. In this study we work | ||
+ | inverse \textbf{m}ixed \textbf{i}nteger \textbf{l}inear \textbf{p}roblems (MILP) | ||
+ | where we seek the objective function coefficients. This is the inverse problem | ||
+ | \cite{AhujaSeptember2001} studied for linear programs (LP). They | ||
+ | show that inverse LP can be solved in polynomial time under mild conditions. We | ||
+ | extend their result for the MILP case. We prove that the decision version of | ||
+ | the inverse MILP is $\coNP$--complete. We also propose a cutting plane algorithm for | ||
+ | solving inverse MILPs for practical purposes. | ||
+ | |||
+ | \ifthenelse{\coralreport = 0}{ | ||
+ | \bigskip\noindent | ||
+ | {\bf Keywords:} Inverse optimization, | ||
+ | computational complexity, polynomial hierarchy | ||
+ | }{} | ||
+ | \end{abstract} | ||
+ | |||
+ | \section{Introduction} | ||
+ | \label{sec: | ||
+ | |||
+ | Optimization problems arise in many fields ... | ||
+ | \end{document} | ||
+ | </ |