Existence Theorems in Vector Optimization with Generalized Order |
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Authors: | Nguyen Quang Huy Do Sang Kim Nguyen Van Tuyen |
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Institution: | 1.Department of Mathematics,Hanoi Pedagogical University 2,Xuan Hoa, Phuc Yen,Vietnam;2.Department of Applied Mathematics,Pukyong National University,Busan,Korea |
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Abstract: | In the present paper, we establish some results for the existence of optimal solutions in vector optimization in infinite-dimensional spaces, where the optimality notion is understood in the sense of generalized order (may not be convex and/or conical). This notion is induced by the concept of set extremality and covers many of the conventional notions of optimality in vector optimization. Some sufficient optimality conditions for optimal solutions of a class of vector optimization problems, which satisfies the free disposal hypothesis, are also examined. |
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