Characterizing robust set containments and solutions of uncertain linear programs without qualifications

Authors:
V. Jeyakumar;Guoyin Li
Affiliations:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
Venue:
Operations Research Letters
Year:
2010

Citing 14
Cited 2

Scenario optimization

Annals of Operations Research
Robust Solutions to Least-Squares Problems with Uncertain Data

SIAM Journal on Matrix Analysis and Applications
Robust Convex Optimization

Mathematics of Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications

Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Set Containment Characterization

Journal of Global Optimization
Mathematical Programming in Data Mining

Data Mining and Knowledge Discovery
Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints

SIAM Journal on Optimization
Dual Characterizations of Set Containments with Strict Convex Inequalities

Journal of Global Optimization
Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

Mathematical Programming: Series A and B
On the stable containment of two sets

Journal of Global Optimization
Some convex programs without a duality gap

Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Duality in robust optimization: Primal worst equals dual best

Operations Research Letters
Robust solutions of uncertain linear programs

Operations Research Letters
Robust linear optimization under general norms

Operations Research Letters

Strong Duality in Robust Convex Programming: Complete Characterizations

SIAM Journal on Optimization
A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Qualification-free dual characterizations are given for robust polyhedral set containments where a robust counterpart of an uncertain polyhedral set is contained in another polyhedral set or a polyhedral set is contained in a robust counterpart of an uncertain polyhedral set. These results are used to characterize robust solutions of uncertain linear programs, where the uncertainty is defined in terms of intervals or l"1-balls. The hidden separable sub-linearity of the robust counterparts allows qualification-free dual characterizations.