Second-Order Optimality Conditions for Multiobjective Optimization Whose Order Induced by Second-Order Cone  

作　　者：Li-Wei Zhang Ji-Hong Zhang Yu-Le Zhang 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China

出　　处：《Journal of the Operations Research Society of China》2018年第2期267-288,共22页中国运筹学会会刊（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Nos.11571059,11731013 and 91330206).

摘　　要：This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.

关 键 词：Second-order cone-induced multiobjective optimization Optimality conditions Polyhedral cone Second-order cone Semi-definite cone 

分 类 号：O17[理学—数学]