Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains |
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| Authors: | N Q Huy N D Yen |
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| Institution: | (1) Department of Mathematics and Informatics, Hanoi Pedagogical University, No. 2, Me Linh, Vinh Phuc, Vietnam;(2) Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam |
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| Abstract: | We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.The authors thank Dr. T. D. Phuong, Dr. T. X. D. Ha, and the referees for helpful comments and suggestions. |
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| Keywords: | Vector optimization strictly quasiconcave functions noncompact feasible domains efficient solution sets contractibility |
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