Optimality conditions in optimization problems with convex feasible set using convexificators

A. Kabgani, M. Soleimani-damaneh, M. Zamani

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper, we consider a nonsmooth optimization problem with a convex feasible set described by constraint functions which are neither convex nor differentiable nor locally Lipschitz necessarily. Utilizing upper regular convexificators, we characterize the normal cone of the feasible set and derive KKT type necessary and sufficient optimality conditions. Under some assumptions, we show that the set of KKT multipliers is bounded. We also characterize the set of optimal solutions and introduce a linear approximation corresponding to the original problem which is useful in checking optimality. The obtained outcomes extend various results existing in the literature to a more general setting.
Original languageEnglish
Pages (from-to)103-121
JournalMathematical Methods of Operations Research
Volume86
DOIs
Publication statusPublished - 2017
Externally publishedYes

Fingerprint

Dive into the research topics of 'Optimality conditions in optimization problems with convex feasible set using convexificators'. Together they form a unique fingerprint.

Cite this