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An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning

Author

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  • Dawan Chumpungam

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Panitarn Sarnmeta

    (KOSEN-KMITL, Bangkok 10520, Thailand)

  • Suthep Suantai

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

In this paper, we introduce a new line search technique, then employ it to construct a novel accelerated forward–backward algorithm for solving convex minimization problems of the form of the summation of two convex functions in which one of these functions is smooth in a real Hilbert space. We establish a weak convergence to a solution of the proposed algorithm without the Lipschitz assumption on the gradient of the objective function. Furthermore, we analyze its performance by applying the proposed algorithm to solving classification problems on various data sets and compare with other line search algorithms. Based on the experiments, the proposed algorithm performs better than other line search algorithms.

Suggested Citation

  • Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2022. "An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1491-:d:806239
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    References listed on IDEAS

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    1. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, June.
    2. Dang Hieu, 2018. "An inertial-like proximal algorithm for equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 399-415, December.
    3. Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
    4. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    5. Adisak Hanjing & Limpapat Bussaban & Suthep Suantai, 2022. "The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
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