Weak sharp minima for piecewise linear multiobjective optimization in normed spaces

Xi Yin Zheng, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)

Abstract

In a general normed space, we consider a piecewise linear multiobjective optimization problem. We prove that a cone-convex piecewise linear multiobjective optimization problem always has a global weak sharp minimum property. By a counter example, we show that the weak sharp minimum property does not necessarily hold if the cone-convexity assumption is dropped. Moreover, under the assumption that the ordering cone is polyhedral, we prove that a (not necessarily cone-convex) piecewise linear multiobjective optimization problem always has a bounded weak sharp minimum property.
Original languageEnglish
Pages (from-to)3771-3779
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume68
Issue number12
DOIs
Publication statusPublished - 15 Jun 2008

Keywords

  • Nonlinear multiobjective optimization
  • Normed space
  • Weak Pareto solution
  • Weak sharp minima

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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