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Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints and Applications

Jiawei Chen(jeky99***at***126.com)
Zhongping Wan(zpwan***at***public.wh.hb.cn)
Zheng Yue(zhengyuestone***at***126.com>)

Abstract: In this work, a nonsmooth multiobjective optimization problem involving generalized invexity with cone constraints and Applications (for short, (MOP)) is considered. The Kuhn-Tucker necessary and sufficient conditions for (MOP) are established by using a generalized alternative theorem of Craven and Yang. The relationship between weakly efficient solutions of (MOP) and vector valued saddle points of its Lagrange function is developed. Furthermore, We investigate the Mond-Weir type duality results for (MOP) and the relationships between weakly efficient solutions of (MOP) and solutions of Hartman-Stampacchia weak vector quasi-variational inequalities (for short, (HSVQI)) and Hartman-Stampacchia nonlinear weak vector quasi-variational inequalities (for short, (HSNVQI)). As an application, we also prove the existence of solutions for (HSVQI) and (HSNVQI) by the Kuhn-Tucker sufficient conditions. These results extend and improve corresponding results of others.

Keywords: Nonsmooth multiobjective optimization problem, Hartman-Stampacchia weak vector quasi-variational inequalities, Hartman-Stampacchia nonlinear weak vector quasi-variational inequalities, Weak (strong, converse)duality, Generalized cone-invex function, Optimality conditions

Category 1: Other Topics (Other )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Report,School of Mathematics and Statistics,Wuhan University

Download: [PDF]

Entry Submitted: 07/02/2010
Entry Accepted: 07/07/2010
Entry Last Modified: 07/02/2010

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