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A New Variant of the Conjugate Descent Method for Solving Unconstrained Optimization Problems and Applications

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  • Aliyu Muhammed Awwal

    (Department of Mathematical Sciences, Faculty of Science, Gombe State University, Gombe 760214, Nigeria
    GSU-Mathematics for Innovative Research Group, Gombe State University, Gombe 760214, Nigeria)

  • Mahmoud Muhammad Yahaya

    (KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Nuttapol Pakkaranang

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Nattawut Pholasa

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

Unconstrained optimization problems have a long history in computational mathematics and have been identified as being among the crucial problems in the fields of applied sciences, engineering, and management sciences. In this paper, a new variant of the conjugate descent method for solving unconstrained optimization problems is introduced. The proposed algorithm can be seen as a modification of the popular conjugate descent (CD) algorithm of Fletcher. The algorithm of the proposed method is well-defined, and the sequence of the directions of search is shown to be sufficiently descending. The convergence result of the proposed method is discussed under the common standard conditions. The proposed algorithm together with some existing ones in the literature is implemented to solve a collection of benchmark test problems. Numerical experiments conducted show the performance of the proposed method is very encouraging. Furthermore, an additional efficiency evaluation is carried out on problems arising from signal processing and it works well.

Suggested Citation

  • Aliyu Muhammed Awwal & Mahmoud Muhammad Yahaya & Nuttapol Pakkaranang & Nattawut Pholasa, 2024. "A New Variant of the Conjugate Descent Method for Solving Unconstrained Optimization Problems and Applications," Mathematics, MDPI, vol. 12(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2430-:d:1450416
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    References listed on IDEAS

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    1. Zhan Wang & Pengyuan Li & Xiangrong Li & Hongtruong Pham, 2020. "A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-14, September.
    2. Luyun Wang & Bo Zhou, 2023. "A Modified Gradient Method for Distributionally Robust Logistic Regression over the Wasserstein Ball," Mathematics, MDPI, vol. 11(11), pages 1-15, May.
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