Convex Directional Derivatives in Optimization

  • D. Ward
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 345)

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.

Keywords

Maximal Element Directional Derivative Constraint Qualification Quasiconvex Function Calculus Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • D. Ward

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