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Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions

Author

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  • Hamiden Abd El-Wahed Khalifa
  • Pavan Kumar

Abstract

This paper introduces cooperative continuous static games (CCSG) with parameters in the cost functions of the players and in the right-hand side of the constraints. The CCSG is converted into the corresponding multi-objective nonlinear programming problem. The resulted nonlinear programming problem is converted into the single objective nonlinear programming problem through the use of the weighted sum method. A solution method for obtaining the stability set of the second kind without differentiability for the CCSG is presented using Karush-Kuhn-Tucker conditions. A numerical example is given for the illustration.

Suggested Citation

  • Hamiden Abd El-Wahed Khalifa & Pavan Kumar, 2023. "Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 46(1), pages 133-147.
    • Handle: RePEc:ids:ijores:v:46:y:2023:i:1:p:133-147
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    Citations

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    Cited by:

    1. Massimiliano Caramia, 2024. "An algorithm to find stable solutions in linear–linear bilevel problems," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 972-988, June.
    2. Miguel F. Arevalo-Castiblanco & Jaime Pachon & Duvan Tellez-Castro & Eduardo Mojica-Nava, 2023. "Cooperative Cruise Control for Intelligent Connected Vehicles: A Bargaining Game Approach," Sustainability, MDPI, vol. 15(15), pages 1-21, August.
    3. Pavan Kumar & Hamiden Abd El-Wahed Khalifa, 2023. "Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness," Mathematics, MDPI, vol. 11(14), pages 1-16, July.

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