A nonlinear Lagrangian approach to constrained optimization problems

Xiaoqi Yang, X. X. Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

65 Citations (Scopus)

Abstract

In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of a path of optimal solutions generated by nonlinear Lagrangian problems and show its convergence toward the optimal set of the original problem. We analyze the convergence of several classes of nonlinear Lagrangian problems in terms of their first and second order necessary optimality conditions.
Original languageEnglish
Pages (from-to)1119-1144
Number of pages26
JournalSIAM Journal on Optimization
Volume11
Issue number4
DOIs
Publication statusPublished - 1 Mar 2001

Keywords

  • Augmented Lagrangian
  • Necessary optimality condition
  • Nonlinear Lagrangian
  • Optimal path
  • Smooth approximate variational principle
  • Zero duality gap

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

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