A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets

CentER Discussion paper Series No. 2012-076

16 Pages Posted: 20 Sep 2012

See all articles by Bram Gorissen

Bram Gorissen

Tilburg University - Tilburg University School of Economics and Management

Aharon Ben-Tal

Technion-Israel Institute of Technology

Hans Blanc

Tilburg University - Tilburg University School of Economics and Management

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: September 19, 2012

Abstract

We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual problem of a robust linear conic program, and then show how to construct the primal robust solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered. We give examples of tractable uncertainty regions that were previously intractable. The results are illustrated by solving a multi-item newsvendor problem. We also propose a new globalized robust counterpart that is more flexible, and is tractable for general convex uncertainty sets and any convex distance function.

Keywords: robust optimization, general convex uncertainty regions, linear conic

JEL Classification: C61

Suggested Citation

Gorissen, Bram and Ben-Tal, Aharon and Blanc, Hans and den Hertog, Dick, A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets (September 19, 2012). CentER Discussion paper Series No. 2012-076. Available at SSRN: https://ssrn.com/abstract=2148956 or http://dx.doi.org/10.2139/ssrn.2148956

Bram Gorissen (Contact Author)

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Aharon Ben-Tal

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Hans Blanc

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

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

Tilburg, 5000 LE
Netherlands

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