A3 Refereed book chapter or chapter in a compilation book

On generalized pseudo- and quasiconvexities for nonsmooth functions




AuthorsVille-Pekka Eronen, Marko M. Mäkelä, Napsu Karmitsa

EditorsRassias T.

PublisherSpringer International Publishing

Publication year2018

Book title Current Research in Nonlinear Analysis. Springer Optimization and Its Applications

Journal name in sourceSpringer Optimization and Its Applications

Volume135

First page 129

Last page155

ISBN978-3-319-89799-8

eISBN978-3-319-89800-1

DOIhttps://doi.org/10.1007/978-3-319-89800-1_6(external)


Abstract

Convexity is the most important and useful concept in mathematical optimization theory. In order to extend the existing results depending on convexity, numerous attempts of generalizing the concept have been published during years. Different types of generalized convexities have proved to be the main tool when constructing optimality conditions, in particular sufficient conditions for optimality. The aim of this paper is to analyze the properties of the generalized pseudo- and quasiconvexities for nondifferentiable locally Lipschitz continuous functions. The treatment is based on the Clarke subdifferentials and generalized directional derivatives.



Last updated on 2024-26-11 at 13:00