Further study on augmented Lagrangian duality theory

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

23 Citations (Scopus)

Abstract

In this paper we present a necessary and sufficient condition for a zero duality gap between a primal optimization problem and its generalized augmented Lagrangian dual problems. The condition is mainly expressed in the form of the lower semicontinuity of a perturbation function at the origin. For a constrained optimization problem a general equivalence is established for zero duality gap properties defined by a general nonlinear Lagrangian dual problem and a generalized augmented Lagrangian dual problem respectively. For a constrained optimization problem with both equality and inequality constraints we prove that first-order and second-order necessary optimality conditions of the augmented Lagrangian problems with a convex quadratic augmenting function converge to that of the original constrained program. For a mathematical program with only equality constraints we show that the second-order necessary conditions of general augmented Lagrangian problems with a convex augmenting function converge to that of the original constrained program.
Original languageEnglish
Pages (from-to)193-210
Number of pages18
JournalJournal of Global Optimization
Volume31
Issue number2
DOIs
Publication statusPublished - 1 Feb 2005

Keywords

  • Augmented Lagrangian
  • Constraint qualification
  • Optimality condition
  • Perturbation function
  • Zero duality gap

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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