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

Indexed by:期刊论文

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE

Volume:14

Issue:3

Page Number:1041-1054

ISSN No.:1547-5816

Key Words:Cone constrained multi-objective optimization; second-order optimality conditions; polyhedral cone; second-order cone; semi-definite cone

Abstract: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.

Date of Publication:2018-07-01