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AIMS Mathematics

2023, Volume 8, Issue 6: 13706-13724. doi: 10.3934/math.2023696
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Research article

A trust-region based an active-set interior-point algorithm for fuzzy continuous Static Games

  • 1.
    Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
  • 2.
    Department of Physics and Engineering Mathematics, Faculty of Engineering-Tanta University, Egypt
  • Received: 27 October 2022 Revised: 17 March 2023 Accepted: 20 March 2023 Published: 10 April 2023

  • MSC : 49N10, 49N35, 65K05, 93D22, 93D52

  • In this paper, a novel treatment for fuzzy continuous static games (FCSGs) is introduced. This treatment is based on the fact that, as well as having a fuzzy number, the fuzziness is applied to the control vectors to deal with high vagueness and imprecision in a continuous static game. The concept of the $ \alpha $-level set used for converting the FCSGs to a deterministic problem $ \alpha $-FCSGs. An active-set strategy is used with Newton's interior point method and a trust-region strategy to insure global convergence for deterministic $ \alpha $-FCSGs problems from any starting point. A reduced Hessian technique is used to overcome the difficulty of having an infeasible trust-region subproblem. The active-set interior-point trust-region algorithm has new features; it is easy to implement and has rapid convergence. Preliminary numerical results are reported.

    Citation: B. El-Sobky, M. F. Zidan. A trust-region based an active-set interior-point algorithm for fuzzy continuous Static Games[J]. AIMS Mathematics, 2023, 8(6): 13706-13724. doi: 10.3934/math.2023696

    Related Papers:

  • In this paper, a novel treatment for fuzzy continuous static games (FCSGs) is introduced. This treatment is based on the fact that, as well as having a fuzzy number, the fuzziness is applied to the control vectors to deal with high vagueness and imprecision in a continuous static game. The concept of the $ \alpha $-level set used for converting the FCSGs to a deterministic problem $ \alpha $-FCSGs. An active-set strategy is used with Newton's interior point method and a trust-region strategy to insure global convergence for deterministic $ \alpha $-FCSGs problems from any starting point. A reduced Hessian technique is used to overcome the difficulty of having an infeasible trust-region subproblem. The active-set interior-point trust-region algorithm has new features; it is easy to implement and has rapid convergence. Preliminary numerical results are reported.


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