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An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Author

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  • Kobkoon Janngam

    (Graduate Ph.D. Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Suthep Suantai

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

Abstract

In this paper, we propose a new accelerated common fixed-point algorithm for two countable families of G -nonexpansive mappings. Weak convergence results are obtained in the context of directed graphs in real Hilbert spaces. As applications, we apply the obtained results to solving some convex minimization problems and employ our proposed algorithm to solve the data classification of Breast Cancer, Heart Diseases and Ionosphere. Moreover, we also compare the performance of our proposed algorithm with other algorithms in the literature and it is shown that our algorithm has a better convergence behavior than the others.

Suggested Citation

  • Kobkoon Janngam & Suthep Suantai, 2022. "An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems," Mathematics, MDPI, vol. 10(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4442-:d:983339
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    References listed on IDEAS

    as
    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    3. Suthep Suantai & Nontawat Eiamniran & Nattawut Pholasa & Prasit Cholamjiak, 2019. "Three-Step Projective Methods for Solving the Split Feasibility Problems," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
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    Cited by:

    1. Kobkoon Janngam & Suthep Suantai & Yeol Je Cho & Attapol Kaewkhao & Rattanakorn Wattanataweekul, 2023. "A Novel Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Classification Problems," Mathematics, MDPI, vol. 11(14), pages 1-15, July.
    2. Rattanakorn Wattanataweekul & Kobkoon Janngam & Suthep Suantai, 2023. "A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery," Mathematics, MDPI, vol. 11(16), pages 1-20, August.

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