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

Authors:
S. K. Zhu;S. J. Li;K. L. Teo
Affiliations:
College of Mathematics and Statistics, Chongqing University, Chongqing, China 401331;College of Mathematics and Statistics, Chongqing University, Chongqing, China 401331 and Mathematical Sciences Research Institute in Chongqing, Chongqing University, Chongqing, China 401331;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845
Venue:
Journal of Global Optimization
Year:
2014

Citing 5
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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.