Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

Duality and penalty methods are popular in optimization. The study on duality and penalty methods for nonconvex multiobjective optimization problems is very limited. In this paper, we introduce vector-valued nonlinear Lagrangian and penalty functions and formulate nonlinear Lagrangian dual problems and nonlinear penalty problems for multiobjective constrained optimization problems. We establish strong duality and exact penalization results. The strong duality is an inclusion between the set of infimum points of the original multiobjective constrained optimization problem and that of the nonlinear Lagrangian dual problem. Exact penalization is established via a generalized calmness-type condition.
Original languageEnglish
Pages (from-to)675-692
Number of pages18
JournalSIAM Journal on Optimization
Volume13
Issue number3
DOIs
Publication statusPublished - 1 Jan 2003

Keywords

  • Duality
  • Exact penalization
  • Multiobjective optimization
  • Nonlinear Lagrangian function
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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