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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]
Copyright of Computational Optimization & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192231984
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  Data: <searchLink fieldCode="DE" term="%22Conjugate+gradient+methods%22">Conjugate gradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Multi-objective+optimization%22">Multi-objective optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Nonconvex+programming%22">Nonconvex programming</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Data: 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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  Data: <i>Copyright of Computational Optimization & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10589-025-00747-z
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      – Code: eng
        Text: English
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        PageCount: 47
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      – SubjectFull: Conjugate gradient methods
        Type: general
      – SubjectFull: Multi-objective optimization
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Nonconvex programming
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      – SubjectFull: Numerical analysis
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      – TitleFull: A nonlinear conjugate gradient algorithm for multiobjective optimization: multiple hybrid search direction and global rates.
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              M: 04
              Text: Apr2026
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              Y: 2026
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