Existence Theorems in Vector Optimization with Generalized Order

Nguyen Quang Huy (), Do Sang Kim () and Nguyen Van Tuyen ()
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Nguyen Quang Huy: Hanoi Pedagogical University 2
Do Sang Kim: Pukyong National University
Nguyen Van Tuyen: Hanoi Pedagogical University 2

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 7, 728-745

Abstract: 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.

Keywords: Vector optimization; Generalized order optimality; Efficient point; Existence theorem; 90C29; 90C30; 90C46; 90C48 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1146-8

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