Optimality Conditions of the Set-valued Optimization Problem with Generalized Co

本文刊于:《Acta Mathematicae Applicatae Sinica》 2018年第1期

关键词:
set-valued maps;generalized cone convexi

Keywords
set-valued maps;generalized cone convexity;Henig proper efficiency;contingent epiderivative;optimality conditions
摘要
     In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.


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