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A Novel Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Classification Problems

Author

Listed:
  • Kobkoon Janngam

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

  • Suthep Suantai

    (Research Center in Optimization and Computational Intelligence for Big Data Prediction, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Yeol Je Cho

    (Department of Mathematics Education, Gyeogsang National University, Jinju 52828, Republic of Korea)

  • Attapol Kaewkhao

    (Research Center in Optimization and Computational Intelligence for Big Data Prediction, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Rattanakorn Wattanataweekul

    (Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand)

Abstract

Fixed-point theory plays many important roles in real-world problems, such as image processing, classification problem, etc. This paper introduces and analyzes a new, accelerated common-fixed-point algorithm using the viscosity approximation method and then employs it to solve convex bilevel optimization problems. The proposed method was applied to data classification with the Diabetes, Heart Disease UCI and Iris datasets. According to the data classification experiment results, the proposed algorithm outperformed the others in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3241-:d:1200849
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    References listed on IDEAS

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    1. Bard, Jonathan F, 1983. "Coordination of a multidivisional organization through two levels of management," Omega, Elsevier, vol. 11(5), pages 457-468.
    2. Sonja Wogrin & Salvador Pineda & Diego A. Tejada-Arango, 2020. "Applications of Bilevel Optimization in Energy and Electricity Markets," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 139-168, Springer.
    3. 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.
    4. Teodora Dan & Patrice Marcotte, 2019. "Competitive Facility Location with Selfish Users and Queues," Operations Research, INFORMS, vol. 67(2), pages 479-497, March.
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