Generalized Semi-Infinite Programming: Optimality Conditions Involving Reverse Convex Problems

Abstract

This article deals with a generalized semi-infinite programming problem (S). Under appropriate assumptions, for such a problem we give necessary and sufficient optimality conditions via reverse convex problems. In particular, a necessary and sufficient optimality condition reduces the problem (S) to a min-max problem constrained with compact convex linked constraints.

Keywords:

• Convex analysis
• Generalized semi-infinite programming problems
• Optimality conditions
• Stability

Mathematics Subject Classification:

• 90C34
• 90C46
• 90C31
• 46N10

Acknowledgments

Part of the special issue, “Variational Analysis and Applications.”