The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some … Read more
In this paper we focus on robust linear optimization problems with uncertainty regions defined by phi-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on phi-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization … Read more
The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some … Read more
We present a constraint-and-column generation algorithm to solve two-stage robust optimization problems. Compared with existing Benders style cutting plane methods, it is a general procedure with a unified approach to deal with optimality and feasibility. A computational study on a two-stage robust location-transportation problem shows that it performs an order of magnitude faster. Also, it … Read more
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be … Read more
Call center scheduling aims to set-up the workforce so as to meet target service levels. The service level depends on the mean rate of arrival calls, which fluctuates during the day and from day to day. The staff scheduling must adjust the workforce period per period during the day, but the flexibility in so doing … Read more
We consider an uncertain variant of the knapsack problem that arises when the exact weight of each item is not exactly known in advance but belongs to a given interval, and the number of items whose weight differs from the nominal value is bounded by a constant. We analyze the worsening of the optimal solution … Read more
We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that “on average” this loss is very small, for an arbitrary compact feasible region. CitationTechnical Report 1479, School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, April 2011ArticleDownload View PDF
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner … Read more
In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by 42 % on average. ArticleDownload … Read more