Hidden Convexity in Partially Separable Optimization

CentER Working Paper Series No. 2011-070

25 Pages Posted: 15 Jun 2011

See all articles by Aharon Ben-Tal

Aharon Ben-Tal

Technion-Israel Institute of Technology

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Monique Laurent

affiliation not provided to SSRN

Date Written: June 10, 2011

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 functions, robust optimization

JEL Classification: C61

Suggested Citation

Ben-Tal, Aharon and den Hertog, Dick and Laurent, Monique, Hidden Convexity in Partially Separable Optimization (June 10, 2011). CentER Working Paper Series No. 2011-070. Available at SSRN: https://ssrn.com/abstract=1865208 or http://dx.doi.org/10.2139/ssrn.1865208

Aharon Ben-Tal

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Dick Den Hertog (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Monique Laurent

affiliation not provided to SSRN ( email )

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