Some properties of approximate solutions for vector optimization problem with set-valued functions

Authors:
Qiusheng Qiu;Xinmin Yang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China and Department of Mathematics, Zhejiang Normal University, Zhejiang, China;Department of Mathematics, Chongqing Normal University, Chongqing, China
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

In this paper, we study the approximate solutions for vector optimization problem with set-valued functions. The scalar characterization is derived without imposing any convexity assumption on the objective functions. The relationships between approximate solutions and weak efficient solutions are discussed. In particular, we prove the connectedness of the set of approximate solutions under the condition that the objective functions are quasiconvex set-valued functions.