Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets

B.L. Gorissen, J.P.C. Blanc, D. den Hertog, A. Ben-Tal

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We propose a new way to derive tractable robust counterparts of a linear program based 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 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 apply the new method to the
globalized robust counterpart scheme and show its tractability.
Original languageEnglish
Pages (from-to)672-679
JournalOperations Research
Volume62
Issue number3
Early online date29 Apr 2014
DOIs
Publication statusPublished - May 2014

Fingerprint

Uncertainty
Linear program
Newsvendor problem
Optimal solution
Duality
Dual problem

Keywords

  • robust optimization
  • general convex uncertainty regions
  • uncertain linear optimizations
  • globalized robust counterpart

Cite this

@article{2351646f874e477e8058498c580d0695,
title = "Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets",
abstract = "We propose a new way to derive tractable robust counterparts of a linear program based 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 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 apply the new method to theglobalized robust counterpart scheme and show its tractability.",
keywords = "robust optimization, general convex uncertainty regions, uncertain linear optimizations, globalized robust counterpart",
author = "B.L. Gorissen and J.P.C. Blanc and {den Hertog}, D. and A. Ben-Tal",
note = "Technical note",
year = "2014",
month = "5",
doi = "10.1287/opre.2014.1265",
language = "English",
volume = "62",
pages = "672--679",
journal = "Operations Research",
issn = "0030-364X",
publisher = "INFORMS Inst.for Operations Res.and the Management Sciences",
number = "3",

}

Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets. / Gorissen, B.L.; Blanc, J.P.C.; den Hertog, D.; Ben-Tal, A.

In: Operations Research, Vol. 62, No. 3, 05.2014, p. 672-679.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets

AU - Gorissen, B.L.

AU - Blanc, J.P.C.

AU - den Hertog, D.

AU - Ben-Tal, A.

N1 - Technical note

PY - 2014/5

Y1 - 2014/5

N2 - We propose a new way to derive tractable robust counterparts of a linear program based 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 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 apply the new method to theglobalized robust counterpart scheme and show its tractability.

AB - We propose a new way to derive tractable robust counterparts of a linear program based 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 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 apply the new method to theglobalized robust counterpart scheme and show its tractability.

KW - robust optimization

KW - general convex uncertainty regions

KW - uncertain linear optimizations

KW - globalized robust counterpart

U2 - 10.1287/opre.2014.1265

DO - 10.1287/opre.2014.1265

M3 - Article

VL - 62

SP - 672

EP - 679

JO - Operations Research

JF - Operations Research

SN - 0030-364X

IS - 3

ER -