Higher order weak epiderivatives and applications to duality and optimality conditions

Authors:
C. R. Chen;S. J. Li;K. L. Teo
Affiliations:
College of Mathematics and Science, Chongqing University, Chongqing, 400030, China;College of Mathematics and Science, Chongqing University, Chongqing, 400030, China;Department of Mathematics and Statistics, Curtin University of Technology, G.P.O. Box U1987, Perth, WA 6845, Australia
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 3
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Generalized second-order contingent epiderivatives in parametric vector optimization problems

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Second-order Karush---Kuhn---Tucker optimality conditions for set-valued optimization

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Abstract

In this paper, the notions of higher order weak contingent epiderivative and higher order weak adjacent epiderivative for a set-valued map are defined. By virtue of higher order weak adjacent (contingent) epiderivatives and Henig efficiency, we introduce a higher order Mond-Weir type dual problem and a higher order Wolfe type dual problem for a constrained set-valued optimization problem (SOP) and discuss the corresponding weak duality, strong duality and converse duality properties. We also establish higher order Kuhn-Tucker type necessary and sufficient optimality conditions for (SOP).