A unified augmented Lagrangian approach to duality and exact penalization

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

79 Citations (Scopus)

Abstract

In this paper, the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real-valued function are established via a generalized augmented Lagrangian and corresponding generalized augmented Lagrangian problems, in which no convexity is imposed on the augmenting function. These results further imply a zero duality gap property between the primal problem and the generalized augmented Lagrangian dual problem. A necessary and sufficient condition for the exact penalty representation in the framework of a generalized augmented Lagrangian is obtained. In the context of constrained programs, we show that generalized augmented Lagrangians present a unified approach to several classes of exact penalization results. Some equivalence among exact penalization results are obtained.
Original languageEnglish
Pages (from-to)533-552
Number of pages20
JournalMathematics of Operations Research
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jan 2003

Keywords

  • Constrained program
  • Duality
  • Exact penalty function
  • Generalized augmented Lagrangian
  • Nonlinear Lagrangian

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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