Optimality conditions for maximizing a locally Lipschitz function

Author: Dutta, Joydeep¹

Source: Optimization, Volume 54, Numbers 4-5, -5/August&U8211;October 2005 , pp. 377-389(13)

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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

Document Type: Research article

DOI: 10.1080/02331930500100213

Affiliations: 1: Department of Mathematics, Indian Institute of Technology, Kanpur – 208106, India