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A Lagrangian Multiplier Theorem of ε weakly Efficient Solutions in Vector Optimization Problems with Set valued Maps

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Author(s): LIAO Wei | ZHAO Ke-quan

Journal: Journal of Chongqing Normal University
ISSN 1672-6693

Volume: 30;
Issue: 6;
Start page: 22;
Date: 2013;
Original page

Keywords: vector optimization with set-valued maps | ε-weakly efficient solutions | Lagrange multiplier theorem

ABSTRACT
" In this paper, we establish a Lagrangian multiplier theorem of ε-weakly efficient solutions in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlike. Firstly, a necessary condition of ε-weakly efficient solutions is given in vector optimization problems with set-valued maps using an alternative theorem. Moreover, a sufficient and necessary condition of ε-weakly efficient solutions is given. Finally, under the assumption of nearly cone-subconvexlike, a Lagrangian multiplier theorem of ε-weakly efficient solutions is established for vector optimization problems with set-valued maps. The main results in this article extend the corresponding results in [6] to the approximate and meanwhile the convexity condition of [6] is reduced to the nearly cone-subconvexlike assumptions."

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