Vector variational inequalities and vector optimization problems on Hadamard manifolds |
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Authors: | Sheng-lan Chen Nan-jing Huang |
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Affiliation: | 1.Department of Mathematics,Sichuan University,Chengdu,People’s Republic of China;2.College of Science,Chongqing University of Posts and Telecommunications,Chongqing,People’s Republic of China |
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Abstract: | In this paper, we introduce a Minty type vector variational inequality, a Stampacchia type vector variational inequality, and the weak forms of them, which are all defined by means of subdifferentials on Hadamard manifolds. We also study the equivalent relations between the vector variational inequalities and nonsmooth convex vector optimization problems. By using the equivalent relations and an analogous to KKM lemma, we give some existence theorems for weakly efficient solutions of convex vector optimization problems under relaxed compact assumptions. |
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