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New hybrid conjugate gradient algorithm for vector optimization problems

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Abstract

Conjugate gradient methods for solving vector optimization problems provide an alternative approach to scalarization techniques that do not require assigning weights to specific objective functions. This paper proposes a hybrid conjugate gradient method as a convex combination of modified Liu–Storey and Dai–Yuan conjugate gradient methods. This approach guarantees a sufficient descent property for the vector search direction and satisfies the Dai–Liao vector conjugacy condition independent of any line search. The global convergence is established using the Wolfe line search without regular restart and assuming convexity on the objective functions. We conducted numerical experiments to showcase the implementation and effectiveness of the proposed hybrid method over the Liu–Storey and Dai–Yuan conjugate gradient methods.

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Acknowledgements

The authors gratefully acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), King Mongkut’s University of Technology Thonburi (KMUTT). This research was funded by the NSRF through the Program Management Unit for Human Resources & Institutional Development, Research, and Innovation [grant number B41G67002]. The first author also acknowledges the support provided by the Petchra Pra Jom Klao PhD scholarship of KMUTT (Contract No. 23/2565). In addition, we sincerely thank anonymous reviewers and associate editor for their invaluable feedback, which has greatly improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTT Fixed Point, Research Laboratory, King Mongkut’s University of Technology Thonburi (KMUTT), Room SCL 802 Fixed Point Laboratory Science Laboratory Building, 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Jamilu Yahaya & Poom Kumam

  2. NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCSCoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Rd, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria

    Jamilu Yahaya

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  1. Jamilu Yahaya
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Correspondence to Poom Kumam.

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Yahaya, J., Kumam, P. New hybrid conjugate gradient algorithm for vector optimization problems. Comp. Appl. Math. 44, 163 (2025). https://doi.org/10.1007/s40314-025-03101-5

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