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

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

Research output: Working paperDiscussion paperOther research output

340 Downloads (Pure)

Abstract

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 [2] 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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages16
Volume2012-076
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-076

Fingerprint

Conic Optimization
Linear Optimization
Optimization Problem
Uncertainty
Newsvendor Problem
Dual Problem
Distance Function
Reformulation
Convex function
Duality
Optimal Solution

Keywords

  • robust optimization
  • general convex uncertainty regions
  • linear conic optimization

Cite this

@techreport{e4c05682e13c4d1abc3fac98ef3c569b,
title = "A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets",
abstract = "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 [2] 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 optimization",
author = "B.L. Gorissen and A. Ben-Tal and J.P.C. Blanc and {den Hertog}, D.",
note = "Pagination: 16",
year = "2012",
language = "English",
volume = "2012-076",
series = "CentER Discussion Paper",
publisher = "Operations research",
type = "WorkingPaper",
institution = "Operations research",

}

A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets. / Gorissen, B.L.; Ben-Tal, A.; Blanc, J.P.C.; den Hertog, D.

Tilburg : Operations research, 2012. (CentER Discussion Paper; Vol. 2012-076).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets

AU - Gorissen, B.L.

AU - Ben-Tal, A.

AU - Blanc, J.P.C.

AU - den Hertog, D.

N1 - Pagination: 16

PY - 2012

Y1 - 2012

N2 - 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 [2] 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.

AB - 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 [2] 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.

KW - robust optimization

KW - general convex uncertainty regions

KW - linear conic optimization

M3 - Discussion paper

VL - 2012-076

T3 - CentER Discussion Paper

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

PB - Operations research

CY - Tilburg

ER -