Volume 55, Number 2, March-April 2021
|Page(s)||841 - 860|
|Published online||16 April 2021|
Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives*
Faculty of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
** Corresponding author: firstname.lastname@example.org
Accepted: 10 March 2021
We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush–Kuhn–Tucker type are established under the second-order constraint qualification. An application to Mond–Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.
Mathematics Subject Classification: 90C26 / 90C46 / 90C48
Key words: Asymptotic contingent epiderivative / optimality conditions / Karush–Kuhn–Tucker multiplier / constraint qualification / duality
© EDP Sciences, ROADEF, SMAI 2021
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