Variable Metric Method for Unconstrained Multiobjective Optimization Problems

doi:10.1007/s40305-022-00447-z

Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (3): 409-438.doi: 10.1007/s40305-022-00447-z

Variable Metric Method for Unconstrained Multiobjective Optimization Problems

Jian Chen¹, Gao-Xi Li², Xin-Min Yang³

1. Department of Mathematics, Shanghai University, Shanghai, 200444, China;
2. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China;
3. National Center for Applied Mathematics of Chongqing, and School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

Received:2022-01-23 Revised:2022-07-15 Online:2023-09-30 Published:2023-09-07
Contact: Xin-Min Yang, Jian Chen, Gao-Xi Li E-mail:xmyang@cqnu.edu.cn;chenjian_math@163.com;ligaoxicn@126.com
Supported by:
This research was supported by the Major Program of the National Natural Science Foundation of China (Nos. 11991020 and 11991024), the National Natural Science Foundation of China (Nos. 11971084 and 12171060), the Natural Science Foundation of Chongqing (No. cstc2019jcyj-zdxmX0016) and Foundation of Chongqing Normal University (Nos. 22XLB005 and 22XLB006).

Abstract

Abstract: In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved that accumulation points of the sequence are Pareto critical points. Then, without convexity assumption, strong convergence is established for the proposed method. Moreover, we use a common matrix to approximate the Hessian matrices of all objective functions, along which a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate. Finally, several numerical results demonstrate the effectiveness of the proposed method.

Key words: Multiobjective optimization, Variable metric method, Pareto point, Superlinear convergence

CLC Number:

90C29
90C30

Jian Chen, Gao-Xi Li, Xin-Min Yang. Variable Metric Method for Unconstrained Multiobjective Optimization Problems[J]. Journal of the Operations Research Society of China, 2023, 11(3): 409-438.

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Variable Metric Method for Unconstrained Multiobjective Optimization Problems

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