Theorems of the alternative and optimization with set-valued maps

X. M. Yang, Xiaoqi Yang, G. Y. Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

52 Citations (Scopus)


In this paper, the concept of generalized cone subconvexlike set-valued maps is presented and a theorem of alternative for the system of generalized inequality-equality set-valued maps is established. By applying the theorem of the alternative and other results, necessary and sufficient optimality conditions for vector optimization problems with generalized cone subconvexlike set-valued maps are obtained.
Original languageEnglish
Pages (from-to)627-640
Number of pages14
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Jan 2000


  • Equivalent conditions
  • Generalized convexity
  • Optimality conditions
  • Set-valued maps
  • Theorem of the alternatives
  • Vector optimization

ASJC Scopus subject areas

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

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