New Generalized Convexity Notion for Set-Valued Maps and Application to Vector Optimization

  • P. H. Sach


In this paper, we introduce a new generalized convexity notion for set-valued maps, called ic-cone-convexlikeness, and use it as the main tool to derive an alternative theorem and necessary conditions for efficient, weakly efficient, and Benson properly efficient solutions of the problem of minimizing a set-valued map subject to set-valued constraints. Our results are valid for a class of optimization problems broader than that of the problems considered in Refs. 1--6 and generalize the corresponding results of these references.


Convexlikeness set-valued maps alternative theorems efficiency Benson proper efficiency 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. H. Sach
    • 1
  1. 1.Professor, Institute of MathematicsHanoiVietnam

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