A class of nonconvex functions and pre-variational inequalities

Xiaoqi Yang, Guang Ya Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

90 Citations (Scopus)

Abstract

A class of nonconvex functions is introduced, called semi-preinvex function, which includes the classes of preinvex functions and arc-connected convex functions. The Fritz-John conditions of the mathematical programming problem are derived for these kinds of functions. The pre-variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions. The Type I function related to unconstrained problems is given as an equivalent form of the pre-variational inequality. Existence theorems for the solution of the pre-variational inequality are also proved.
Original languageEnglish
Pages (from-to)359-373
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume169
Issue number2
DOIs
Publication statusPublished - 15 Sep 1992
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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