A3 Book chapter
On generalized pseudo- and quasiconvexities for nonsmooth functions




List of Authors: Ville-Pekka Eronen, Marko M. Mäkelä, Napsu Karmitsa
Publisher: Springer International Publishing
Publication year: 2018
Book title *: Current Research in Nonlinear Analysis. Springer Optimization and Its Applications
Journal name in source: Springer Optimization and Its Applications
Volume number: 135
ISBN: 978-3-319-89799-8
eISBN: 978-3-319-89800-1

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 2019-20-07 at 08:11