Efficiency and approachability of nonconvex bicriteria programs

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this paper we investigate equivalences between an efficient solution of a bicriteria program and a lower envelope point of a certain image set of the bicriteria program. We also employ various kinds of approachabilities to characterize efficiency and proper efficiency for nonconvex bicriteria programs. In particular, nonlinear Lagranian functions are applied to construct dual problems and to study stability for the corresponding constrained scalar optimization problems. Under certain conditions we show that the finite approachability, proper efficiency, stability, and exact penalization of the relevant constrained scalar optimization problems are equivalent.
Original languageEnglish
Pages (from-to)134-150
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume261
Issue number1
DOIs
Publication statusPublished - 1 Sep 2001

Keywords

  • Approachability
  • Bicriteria program
  • Efficiency
  • Exact penalization
  • Nonlinear Lagrangian
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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