Globalized Robust Optimization for Nonlinear Uncertain Inequalities

CentER Discussion Paper Series No. 2015-031

29 Pages Posted: 16 Jun 2015

See all articles by Aharon Ben-Tal

Aharon Ben-Tal

Technion-Israel Institute of Technology

R.C.M. Brekelmans

Tilburg University - Tilburg University School of Economics and Management

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Jean-Philippe Vial

University of Geneva

Date Written: June 15, 2015

Abstract

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem’s parameters. The classical robust counterpart (RC) of the problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set, and offers no guarantees for parameter values outside this uncertainty set. The globalized robust counterpart (GRC) extends this idea by allowing controlled constraint violations in a larger uncertainty set. The constraint violations are controlled by the distance of the parameter to the original uncertainty set. We derive tractable GRCs that extend the initial GRCs in the literature: our GRC is applicable to nonlinear constraints instead of only linear or conic constraints, and the GRC is more flexible with respect to both the uncertainty set and distance measure function, which are used to control the constraint violations. In addition, we present a GRC approach that can be used to provide an extended trade-off overview between the objective value and several robustness measures.

Keywords: robust optimization, globalized robust counterpart, constraint

JEL Classification: C61, C63, M11

Suggested Citation

Ben-Tal, Aharon and Brekelmans, R.C.M. and den Hertog, Dick and Vial, Jean-Philippe, Globalized Robust Optimization for Nonlinear Uncertain Inequalities (June 15, 2015). CentER Discussion Paper Series No. 2015-031. Available at SSRN: https://ssrn.com/abstract=2618429 or http://dx.doi.org/10.2139/ssrn.2618429

Aharon Ben-Tal (Contact Author)

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

R.C.M. Brekelmans

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

P.O. Box 90153
B 1029
5000 LE Tilburg
Netherlands
+31 13 466 8234 (Phone)

Dick Den Hertog

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

Tilburg, 5000 LE
Netherlands

Jean-Philippe Vial

University of Geneva ( email )

102 Bd Carl-Vogt
Genève, CH - 1205
Switzerland
(41) 22 705 81 24 (Phone)
(41) 22 705 81 04 (Fax)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
79
Abstract Views
426
rank
321,945
PlumX Metrics