Title: Convex Directional Derivatives in Optimization
Abstract: Broadly speaking, a generalized convex function is one which has some property of convex functions that is essential in a particular application. Two such properties are convexity of lower level sets (in the case of quasiconvex functions) and convexity of the ordinary directional derivative as a function of direction (in the case of Pshenichnyi’s quasidifferentiable functions). In recent years, several directional derivatives have been defined that, remarkably, are always convex as a function of direction. This means that all functions are “generalized convex” in the sense that they have certain convex directional derivatives. As a result, it has become worthwhile to develop generalizations of the Fritz John and Kuhn-Tucker optimality conditions in terms of the subgradients of convex directional derivatives. In this paper, we derive some general versions of these conditions for an inequality-constrained, nondifferentiable, nonconvex mathematical program.
Publication Year: 1990
Publication Date: 1990-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 6
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