SECOND-ORDER OPTIMALITY CONDITIONS FOR CONE CONSTRAINED MULTI-OBJECTIVE OPTIMIZATION

被引：1
|
作者：
Zhang, Liwei [1 ]
Zhang, Jihong [1 ]
Zhang, Yule [1 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
来源：
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2018年 / 14卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Cone constrained multi-objective optimization; second-order optimality conditions; polyhedral cone; second-order cone; semi-definite cone; OBJECTIVE OPTIMIZATION; QUALIFICATIONS;
D O I：
10.3934/jimo.2017089
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The aim of this paper is to develop second-order necessary and second-order sufficient optimality conditions for cone constrained multiobjective optimization. First of all, we derive, for an abstract constrained multi-objective optimization problem, two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions. Secondly, basing on the optimality results for the abstract problem, we demonstrate, for cone constrained multi-objective optimization problems, the first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as the second-order sufficient optimality conditions under upper second-order regularity for the conic constraint. Finally, using the optimality conditions for cone constrained multi-objective optimization obtained, we establish optimality conditions for polyhedral cone, second-order cone and semi-definite cone constrained multi-objective optimization problems.
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页码：1041 / 1054
页数：14
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