IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3241-d1200849.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3241/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3241/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jalili Marand, Ata & Hoseinpour, Pooya, 2024. "A congested facility location problem with strategic customers," European Journal of Operational Research, Elsevier, vol. 318(2), pages 442-456.
    2. Fadda, Edoardo & Manerba, Daniele & Cabodi, Gianpiero & Camurati, Paolo Enrico & Tadei, Roberto, 2021. "Comparative analysis of models and performance indicators for optimal service facility location," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    3. Sneha Dhyani Bhatt & Sachin Jayaswal & Ankur Sinha & Navneet Vidyarthi, 2021. "Alternate second order conic program reformulations for hub location under stochastic demand and congestion," Annals of Operations Research, Springer, vol. 304(1), pages 481-527, September.
    4. Bhatt, Sneha Dhyani & Sinha, Ankur & Jayaswal, Sachin, 2024. "The capacitated r-hub interdiction problem with congestion: Models and solution approaches," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 185(C).
    5. Ahlatcioglu, Mehmet & Tiryaki, Fatma, 2007. "Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems," Omega, Elsevier, vol. 35(4), pages 432-450, August.
    6. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.
    7. Kovács, András & Egri, Péter & Kis, Tamás & Váncza, József, 2013. "Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem," International Journal of Production Economics, Elsevier, vol. 143(2), pages 385-394.
    8. Puchit Sariddichainunta & Masahiro Inuiguchi, 2017. "Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function," Annals of Operations Research, Springer, vol. 256(2), pages 285-304, September.
    9. Holger Heitsch & René Henrion & Thomas Kleinert & Martin Schmidt, 2022. "On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints," Journal of Global Optimization, Springer, vol. 84(3), pages 651-685, November.
    10. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    11. Iacocca, Kathleen & Mahar, Stephen & Daniel Wright, P., 2022. "Strategic horizontal integration for drug cost reduction in the pharmaceutical supply chain," Omega, Elsevier, vol. 108(C).
    12. G. Constante-Flores & A. J. Conejo & S. Constante-Flores, 2022. "Solving certain complementarity problems in power markets via convex programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 465-491, October.
    13. Zhang, Wenwei & Xu, Min & Wang, Shuaian, 2023. "Joint location and pricing optimization of self-service in urban logistics considering customers’ choice behavior," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    14. Çalcı, Baturay & Leibowicz, Benjamin D. & Bard, Jonathan F. & Jayadev, Gopika G., 2024. "A bilevel approach to multi-period natural gas pricing and investment in gas-consuming infrastructure," Energy, Elsevier, vol. 303(C).
    15. Calvete, Herminia I. & Galé, Carmen, 2011. "On linear bilevel problems with multiple objectives at the lower level," Omega, Elsevier, vol. 39(1), pages 33-40, January.
    16. Klein, Michael G. & Verter, Vedat & Moses, Brian G., 2020. "Designing a rural network of dialysis facilities," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1088-1100.
    17. Teodora Dan & Andrea Lodi & Patrice Marcotte, 2020. "Joint location and pricing within a user-optimized environment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 61-84, March.
    18. Xu, Xianhao & Shen, Yaohan & (Amanda) Chen, Wanying & Gong, Yeming & Wang, Hongwei, 2021. "Data-driven decision and analytics of collection and delivery point location problems for online retailers," Omega, Elsevier, vol. 100(C).
    19. Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.
    20. Polyxeni-Margarita Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development," Journal of Global Optimization, Springer, vol. 60(3), pages 425-458, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3241-:d:1200849. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.