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

P. H. Sach
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P. H. Sach: Professor, Institute of Mathematics

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 1, No 8, 157-179

Abstract: Abstract 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.

Keywords: Convexlikeness; set-valued maps; alternative theorems; efficiency; Benson proper efficiency (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1716-4

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