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Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations

Author

Listed:
  • A.M. Ramos

    (Universidad Complutense de Madrid)

  • R. Glowinski

    (Université P. et M. Curie
    University of Houston)

  • J. Periaux

    (Dassault Aviation)

Abstract

This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate-gradient algorithms for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.

Suggested Citation

  • A.M. Ramos & R. Glowinski & J. Periaux, 2002. "Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 457-498, March.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:3:d:10.1023_a:1017981514093
    DOI: 10.1023/A:1017981514093
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    References listed on IDEAS

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    1. A.M. Ramos & R. Glowinski & J. Periaux, 2002. "Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 499-516, March.
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    Cited by:

    1. Zhao, Hengzhi & Zhang, Jiwei & Lu, Jing, 2023. "Numerical approximate controllability for unidimensional parabolic integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 575-596.
    2. A.M. Ramos & R. Glowinski & J. Periaux, 2002. "Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 499-516, March.
    3. Miguel R. Nuñez-Chávez & Juan B. Límaco Ferrel, 2023. "Hierarchical Controllability for a Nonlinear Parabolic Equation in One Dimension," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 1-48, July.
    4. Axel Dreves & Joachim Gwinner, 2016. "Jointly Convex Generalized Nash Equilibria and Elliptic Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1065-1086, March.

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