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A nonlinear conjugate gradient algorithm for multiobjective optimization: multiple hybrid search direction and global rates.

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Title: A nonlinear conjugate gradient algorithm for multiobjective optimization: multiple hybrid search direction and global rates.
Authors: He, Qing-Rui1 (AUTHOR) heqr1998@163.com, Li, Sheng-Jie1,2 (AUTHOR) lisj@cqu.edu.cn, Li, Ming-Hua3 (AUTHOR) minghuali20021848@163.com, Chen, Chun-Rong1,2 (AUTHOR) chencr1981@163.com
Source: Computational Optimization & Applications. Apr2026, Vol. 93 Issue 3, p1021-1067. 47p.
Subjects: Conjugate gradient methods, Multi-objective optimization, Algorithms, Nonconvex programming, Numerical analysis
Abstract: Conjugate gradient (CG) methods for multiobjective optimization update search directions by combining the multiobjective steepest descent direction and the last search direction. In this paper, we incorporate some customized techniques with multiobjective characteristics into this combination rule and call an associated implementation the multiple hybrid search direction (MHSD). A novel nonlinear CG algorithm with MHSD for multiobjective optimization is then proposed and investigated. We also extend a well-known improved Wolfe line search to the multiobjective setting and, with it, establish a global convergence result. Moreover, under technical assumptions, the rate of convergence for non-convex and strongly convex vector-valued functions is analyzed. Additionally, we consider a variant of the algorithm, which has a stronger global convergence. Numerical comparisons with other state-of-the-art CG-type algorithms show that the presented algorithms are promising. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:Conjugate gradient (CG) methods for multiobjective optimization update search directions by combining the multiobjective steepest descent direction and the last search direction. In this paper, we incorporate some customized techniques with multiobjective characteristics into this combination rule and call an associated implementation the multiple hybrid search direction (MHSD). A novel nonlinear CG algorithm with MHSD for multiobjective optimization is then proposed and investigated. We also extend a well-known improved Wolfe line search to the multiobjective setting and, with it, establish a global convergence result. Moreover, under technical assumptions, the rate of convergence for non-convex and strongly convex vector-valued functions is analyzed. Additionally, we consider a variant of the algorithm, which has a stronger global convergence. Numerical comparisons with other state-of-the-art CG-type algorithms show that the presented algorithms are promising. [ABSTRACT FROM AUTHOR]
ISSN:09266003
DOI:10.1007/s10589-025-00747-z