The semi-E cone convex set-valued map and its applications |
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| Authors: | Zhi-Ang Zhou Xin-Min Yang Xuan Wan |
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| Affiliation: | 1.College of Sciences,Chongqing University of Technology,Chongqing,China;2.College of Mathematical Sciences,Chongqing Normal University,Chongqing,China;3.Department of Foundation,Chongqing Telecommunication Polytechnic College,Chongqing,China |
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| Abstract: | In this paper, firstly, a new notion of the semi-E cone convex set-valued map is introduced in locally convex spaces. Secondly, without any convexity assumption, we investigate the existence conditions of the weakly efficient element of the set-valued optimization problem. Finally, under the assumption of the semi-E cone convexity of set-valued maps, we obtain that the local weakly efficient element of the set-valued optimization problem is the weakly efficient element. We also give some examples to illustrate our results. |
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