On the stable containment of two sets

Authors:
Miguel A. Goberna;Virginia N. Vera De Serio
Affiliations:
Department of Statistics and Operations Research, Universidad de Alicante, Alicante, Spain 03071;Faculty of Economics, Universidad Nacional de Cuyo, Mendoza, Argentina 5500
Venue:
Journal of Global Optimization
Year:
2008

Citing 4
Cited 1

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

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

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies the stability of the set containment problem. Given two non-empty sets in the Euclidean space which are the solution sets of two systems of (possibly infinite) inequalities, the Farkas type results allow to decide whether one of the two sets is contained or not in the other one (which constitutes the so-called containment problem). In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the two sets is preserved by sufficiently small perturbations or not. This paper deals with this stability problem as a particular case of the maintaining of the relative position of the images of two set-valued mappings; first for general set-valued mappings and second for solution sets mappings of convex and linear systems. Thus the results in this paper could be useful in the postoptimal analysis of optimization problems with inclusion constraints.