Vector optimization problems with nonconvex preferences |
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Authors: | N J Huang A M Rubinov X Q Yang |
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Institution: | (1) Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China;(2) Centre for Informations and Applied Optimization, University of Ballarat, Ballarat, Vic, 3353, Australia;(3) Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China |
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Abstract: | In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex
cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational
inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems
is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones
depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of
vector complementarity problems, vector variational inequalities, and minimal element problems are also given.
While this paper was being revised in September 2006, Professor Alex Rubinov (the second author of the paper) left us due
to the illness. This is a very sad news to us. We dedicate this paper to the memory of Professor Rubinov as a mathematician
and truly friend. |
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Keywords: | Vector complementarity problem vector variational inequality vector optimization problem nonconvex cone |
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