Global Convergence of a Modified BFGS-Type Method Based on Function Information for Nonconvex Multiobjective Optimization Problems

doi:10.1007/s40305-025-00589-w

Abstract

Abstract: Most of the quasi-Newton methods for multiobjective optimization require independent approximations of the Hessian matrix for each objective function at each iteration, which leads to significant storage and computational burdens. To address this issue, in this paper, we propose a novel modified BFGS-type method for nonconvex multiobjective optimization problems (M-BFGSMO) based on function information. The M-BFGSMO framework utilizes a shared BFGS-type matrix to approximate the Hessian matrix of all objective functions simultaneously, updating it iteratively using gradient and function value information from previous iterations. This approach balances computational efficiency with algorithmic performance. We establish the convergence of the M-BFGSMO method without the requirement of convexity, and prove its R-linear convergence under mild conditions. Numerical experiments on test problems, including both convex and nonconvex cases, demonstrate the effectiveness and computational advantages of the proposed method compared to some existing approaches.

Key words: Nonconvex multiobjective optimization, Modified BFGS-type method, Wolfe line search, Global convergence

CLC Number:

65K05·90C29·90C30·90C53

Ying-Xue Yang, Xin Deng, Li-Ping Tang. Global Convergence of a Modified BFGS-Type Method Based on Function Information for Nonconvex Multiobjective Optimization Problems[J]. Journal of the Operations Research Society of China, 2026, 14(3): 1014-1037.

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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-025-00589-w

https://www.jorsc.shu.edu.cn/EN/Y2026/V14/I3/1014

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Global Convergence of a Modified BFGS-Type Method Based on Function Information for Nonconvex Multiobjective Optimization Problems

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