Optimality conditions for maximizing a locally Lipschitz function

Abstract

In this article we intend to study the necessary and sufficient conditions for global maximization of locally Lipschitz functions. We develop a necessary and sufficient condition for a class of Lipschitz pseudoconvex function in terms of the Clarke subdifferential. We also develop sufficient conditions for optimality in terms of very general non-smooth objects called convexifactors.

Keywords:

• Locally Lipschitz function
• Lipschitz pseudoconvex function
• Clarke subdifferential
• Optimality conditions
• Convexifactors
• Mathematics Subject Classifications 2000: 26B25
• 26B35
• 49J52
• 49K99
• 90C25

Acknowledgments

The author is grateful to Professor J. E. Martinez-Legaz for useful discussions and also providing the Example 2.1. The author is also grateful to the anonymous referee, whose suggestions have vastly enhanced the presentation of the article.

Notes

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.

Additional information

Notes on contributors

Joydeep Dutta

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.