Duality and exact penalization for vector optimization via augmented Lagrangian

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)

Abstract

In this paper, we introduce an augmented Lagrangian function for a multiobjective optimization problem with an extended vector-valued function. On the basis of this augmented Lagrangian, set-valued dual maps and dual optimization problems are constructed. Weak and strong duality results are obtained. Necessary and sufficient conditions for uniformly exact penalization and exact penalization are established. Finally, comparisons of saddle-point properties are made between a class of augmented Lagrangian functions and nonlinear Lagrangian functions for a constrained multiobjective optimization problem.
Original languageEnglish
Pages (from-to)615-640
Number of pages26
JournalJournal of Optimization Theory and Applications
Volume111
Issue number3
DOIs
Publication statusPublished - 1 Dec 2001

Keywords

  • Augmented lagrangian
  • Duality
  • Exact penalization, nonlinear lagrangian
  • Vector optimization

ASJC Scopus subject areas

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

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