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Connectedness of Benson proper efficiency in vector top base optimization of set valued maps

SHENG Bao huai,LIU San yang (School of Science, Xidian Univ., Xi′an 710071, China)  
Connectedness of Benson proper efficient set and Benson proper efficient solution set of vector optimization of set valued maps are investigated. The results obtained actually imply that the Benson proper efficient set of the objective space is connected when the objective function is cone subconvexlike, and that if the objective function is a cone convex set valued mapping, the Benson proper efficient solution set is connected too. As an interesting application of the results, the connectednesses of the Benson proper efficient set and the Benson proper efficient solution set for the vector top base optimization of set valued maps are obtained.
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