Semi-infinite programming, duality, discretization and optimality conditions†

†Invited survey.

Abstract

The aim of this article is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first- and second-order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.

†Invited survey.

Keywords:

• semi-infinite programming
• conjugate duality
• convex analysis
• discretization
• Lagrange multipliers
• first- and second-order optimality conditions

Acknowledgements

The author would like to thank Frederic Bonnans for a discussion of second-order optimality conditions, and Diethard Klatte and an anonymous referee for many helpful suggestions. This work was supported in part by the National Science Foundation award DMI-0619977.

Notes

†Invited survey.

Note

1. All subdifferentials and gradients are taken here with respect to x.