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

J. Vicente-Pérez, M. Rodríguez Álvarez

The strong Slater condition plays a significant role in the stability analysis of linear semi-infinite inequality systems. In this work, we study the strong Slater condition of a given linear inequality system with an evenly convex constraint set X. In other words, we deal with the stability of the intersection of a given evenly convex set with the solution set of a linear system whose coefficients can be arbitrarily perturbed. To this aim, we firstly focus on the case where X is a closed convex set, and then we derive the more general case where X is evenly convex. We establish dual characterizations for the aforementioned set of strong Slater points in terms of the data of both the linear system and the constraint set, following similar characterizations of the solution set of a given linear system.

Keywords: Strong Slater condition, Linear inequality system, Duality, Stability

GT13.OPTCONT6 Invited Session
November 7, 2023  11:40 AM
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