Optimality conditions for vector optimization problem governed by the cone constrained generalized equations. (4th May 2019)

• Record Type: Journal Article
• Authors: Pang, Li-Ping; Meng, Fan-Yun; Xiao, Ze-Hao; Xu, Na
• Is Part Of: Optimization. Volume 68:Number 5(2019)
• Page Start: 921
• Page End: 954
• Publication Date: 2019-05-04
• Subjects: Optimality conditions -- vector optimization -- generalized equations -- second-order cone; 90C46 -- 90C29 -- 90C31 -- 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1561693
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The paper considers a class of vector optimization problems with cone constrained generalized equations. By virtue of advanced tools of variational analysis and generalized differentiation, a limiting normal cone of the graph of the normal cone constrained by the second-order cone is obtained. Based on the calmness condition, we derive an upper estimate of the coderivative for a composite set-valued mapping. The necessary optimality condition for the problem is established under the linear independent constraint qualification. As a special case, the obtained optimality condition is simplified with the help of strict complementarity relaxation conditions. The numerical results on different examples are given to illustrate the efficiency of the optimality conditions.