On the strong Slater condition of linear systems with an evenly convex constraint set

Abstract

This paper deals with the stability of the intersection of a given evenly convex set $X$ with the solution set of a given linear system $\sigma$ whose coefficients can be arbitrarily perturbed. More precisely, we focus on the set of strong Slater points of $\sigma$ in $X$, by analyzing firstly the case when $X$ is a closed convex set, and then the more general case when $X$ is evenly convex. We shall establish dual characterizations for the aforementioned set of strong Slater points by following well-known characterizations of the solution set of a linear system. Finally, we apply our results to analyze the consistency of systems with both strict and weak inequalities defined by lower semicontinuous convex functions.