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A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization

Author

Listed:
  • Jiawei Chen

    (Southwest University)

  • Yushan Bai

    (Southwest University)

  • Guolin Yu

    (North Minzu University)

  • Xiaoqing Ou

    (North Minzu University
    College of Management, Chongqing College of Humanities, Science & Technology)

  • Xiaolong Qin

    (Hangzhou Normal University
    Nanjing Center for Applied Mathematics)

Abstract

A novel Polak-Ribière-Polyak (PRP) type conjugate gradient method is proposed to solve a nonconvex vector optimization. This variant is a nontrivial extension of a PRP type conjugate gradient method from the scalar case to the vector case. We construct a new nonnegative conjugate parameter avoiding the usual truncation of conjugate gradient method. The search direction in the new PRP type conjugate gradient method is proved to satisfy the sufficient descent condition without involving any line search. The globally convergent results of the novel conjugate gradient method are derived under the standard Wolfe line search as well as the Armijo line search strategy without convexity assumption of the objective functions. Besides, the iterative sequence generated by the proposed method is also proved to be weakly convergent to some weak Pareto optimal solution of the vector optimization problem under the cone-pseudoconvexity assumption. Numerical experiments also manifest the validity of the proposed novel method. The gained results improve the corresponding results of (SIAM J Optim 28:2690–2720, 2018 and Comput Optim Appl 86:457–489, 2023).

Suggested Citation

  • Jiawei Chen & Yushan Bai & Guolin Yu & Xiaoqing Ou & Xiaolong Qin, 2025. "A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-30, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02571-7
    DOI: 10.1007/s10957-024-02571-7
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    References listed on IDEAS

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    1. Jiawei Chen & Elisabeth Köbis & Markus Köbis & Jen-Chih Yao, 2018. "Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 816-834, June.
    2. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
    3. Gravel, Marc & Martel, Jean Marc & Nadeau, Raymond & Price, Wilson & Tremblay, Richard, 1992. "A multicriterion view of optimal resource allocation in job-shop production," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 230-244, August.
    4. M. L. N. Gonçalves & L. F. Prudente, 2020. "On the extension of the Hager–Zhang conjugate gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 889-916, July.
    5. C. Hillermeier, 2001. "Generalized Homotopy Approach to Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 557-583, September.
    6. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.
    7. Madjid Tavana & Mariya Sodenkamp & Leena Suhl, 2010. "A soft multi-criteria decision analysis model with application to the European Union enlargement," Annals of Operations Research, Springer, vol. 181(1), pages 393-421, December.
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