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Hidden convexity in partially separable optimization

Aharon Ben-Tal(abental***at***ie.technion.ac.il)
Dick Den Hertog(D.denHertog***at***uvt.nl)
Monique Laurent(M.Laurent***at***cwi.nl)

Abstract: 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 partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.

Keywords: convex relaxation of nonconvex problems, hidden convexity, partially separable

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Robust Optimization

Category 3: Nonlinear Optimization (Quadratic Programming )

Citation: CentER Discussion Paper CDP-070, June 2011, CentER, Tilburg University, Department of Econometrics and Operations Research, 5000 LE Tilburg, Netherlands

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Entry Submitted: 06/27/2011
Entry Accepted: 06/27/2011
Entry Last Modified: 06/27/2011

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