Optimality conditions via exact penalty functions

K. W. Meng, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

In this paper, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using lp penalty functions, with 0 < p < 1. We introduce some optimality indication sets by using contingent derivatives of penalty function terms. Some characterizations of optimality indication sets are obtained by virtue of the original problem data. We show that the KKT optimality condition holds at a feasible point if this point is a local minimizer of some lp penalty function with p belonging to the optimality indication set. Our result on constrained nonlinear programming includes some existing results from the literature as special cases.
Original languageEnglish
Pages (from-to)3208-3231
Number of pages24
JournalSIAM Journal on Optimization
Volume20
Issue number6
DOIs
Publication statusPublished - 1 Dec 2010

Keywords

  • Exact penalty function
  • KKT optimality condition
  • Mathematical programs with complementarity constraints
  • Mordukhovich stationarity
  • Nonlinear programming problem
  • Strong stationarity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

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