The set of strong Slater points of a linear semi-infinite system
M. Rodríguez Álvarez, J. Vicente-Pérez
The strong Slater condition plays a significant role in the stability analysis of linear
semi-infinite inequality systems. In this work, we study 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 characterizacions 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.
Keywords: Linear semi-infinite system, Strong Slater points.
Scheduled
GT11 Continuous Optimization I
June 9, 2022 10:10 AM
A12
Other papers in the same session
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J. Castro, L. F. Escudero, J. F. Monge
J. Camacho Moro, M. J. Cánovas Cánovas, J. Parra López
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