The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces

Xiyin Zheng, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)

Abstract

In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.
Original languageEnglish
Pages (from-to)1243-1256
Number of pages14
JournalScience in China, Series A: Mathematics
Volume51
Issue number7
DOIs
Publication statusPublished - 1 Jul 2008

Keywords

  • Connectedness
  • Normed space
  • Piecewise linear function
  • Weak Pareto solution

ASJC Scopus subject areas

  • Mathematics(all)

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