Stability Theory for Linear Inequality Systems
SIAM Journal on Matrix Analysis and 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
Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems
Mathematical Programming: Series A and B
Dual Characterizations of Set Containments with Strict Convex Inequalities
Journal of Global Optimization
New descent rules for solving the linear semi-infinite programming problem
Operations Research Letters
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Many mathematical programming models arising in practice present a block structure in their constraint systems. Consequently, the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not. The existence theorems allow to decide when the intersection of non-empty sets in the Euclidean space, which are the solution sets of systems of (possibly infinite) inequalities, is empty or not. 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 sets is preserved by sufficiently small perturbations or not. This paper focuses on the stability of the non-empty (empty) intersection of the solutions of some given systems, which can be seen as the images of set-valued mappings. We give sufficient conditions for the stability, and necessary ones as well; in particular we consider (semi-infinite) convex systems and also linear systems. In this last case we discuss the distance to ill-posedness.