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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The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11171237, 11471230).
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Chen, Sl., Huang, Nj. Vector variational inequalities and vector optimization problems on Hadamard manifolds. Optim Lett 10, 753–767 (2016). https://doi.org/10.1007/s11590-015-0896-1
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DOI: https://doi.org/10.1007/s11590-015-0896-1