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$\varepsilon-$Strictly Subdifferential of Set-valued Map and Its Application

Yu Li (yulilyy***at***163.com)

Abstract: In this paper, firstly, the concept of $\varepsilon-$strictly efficient subdifferential for set-valued map is introduced in Hausdorff locally convex topological vector spaces. Secondly, a characterization of this subdifferential by scalarization and the generalized $\varepsilon-$ Moreau-Rockafellar type theorem for set-valued maps are established. Finally, the necessary optimality condition of the constraint set-valued optimization problem for $\varepsilon-$ strictly efficient solutions is obtained in terms of Lagrange multiplier by using the concept of $\varepsilon-$ strictly efficient subdifferential for set-valued map.

Keywords: set-valued map;~~$\varepsilon-$strictly efficiency; ~~subdifferential;~~$\varepsilon-$ Moreau-Rockafellar type theorem ~~ Lagrange multiplier;

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: 16,Institute of Mathematics and Computer of Science, Yichun University,Yichun 336000,China;2015

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Entry Submitted: 05/26/2015
Entry Accepted: 05/26/2015
Entry Last Modified: 05/26/2015

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