Abstract
AbstractThe strong Slater condition plays a significant role in the stability analysis of linear semi-infinite inequality systems. This piece of work studies the set of strong Slater points, whose non-emptiness guarantees the fullfilment of the strong Slater condition. Given a linear inequality system, we firstly establish some basic properties of the set of strong Slater points. Then, we derive dual characterizations for this set in terms of the data of the system, following similar characterizations provided also for the set of Slater points and the solution set of the given system, which are based on the polarity operators for evenly convex and closed convex sets. Finally, we present two geometric interpretations and apply our results to analyze the strict inequality systems defined by lower semicontinuous convex functions.
Funder
Ministerio de Ciencia, Innovación y Universidades
Generalitat Valenciana
Universidad de Alicante
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Analysis
Reference27 articles.
1. Barbara, A., Crouzeix, J.P.: Concave gauge functions and applications. Math. Methods Oper. Res. 40, 43–74 (1994)
2. Brosowski, B.: Parametric semi-infinite linear programming I. Continuity of the feasible set and of the optimal value. Math. Programm. Study 21, 18–42 (1984)
3. Christov, G., Todorov, M.: Semi-infinite optimization: existence and uniqueness of the solution. Math. Balkanica 2, 182–191 (1988)
4. Fajardo, M.D., Goberna, M.A., Rodríguez, M.M.L., Vicente-pérez, J.: Even convexity and optimization: handling strict inequalities. Springer Cham (2020)
5. Fan, K.: On infinite systems of linear inequalities. J. Math. Anal. Appl. 21, 475–478 (1968)