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

S. Zhu (), S. Li () and K. Teo ()

Journal of Global Optimization, 2014, vol. 58, issue 4, 673-692

Abstract: In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the Kurcyusz–Robinson–Zowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order Karush–Kuhn–Tucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order Kurcyusz–Robinson–Zowe regularity assumption. Copyright Springer Science+Business Media New York 2014

Keywords: Set-valued optimization; Second-order composed contingent derivative; Lagrange multiplier rule; Karush–Kuhn–Tucker condition; Regularity assumption; Optimality conditions; 49J53; 49K30; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-013-0067-9

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