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Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach

  • A.M. Ramos
  • R. Glowinski
  • J. Periaux
Article

Abstract

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.

Burgers equation pointwise control Nash equilibria adjoint systems Dirac measures quasi-Newton algorithms single-objective control problems multiobjective control problems 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A.M. Ramos
    • 1
  • R. Glowinski
    • 2
    • 3
  • J. Periaux
    • 4
  1. 1.Departamento de Matemática AplicadaUniversidad Complutense de MadridMadridSpain
  2. 2.Laboratoire d'Analyse NumériqueUniversité Pierre et Marie CurieParisFrance
  3. 3.Department of MathematicsUniversity of HoustonHouston
  4. 4.Dassault AviationSaint Cloud

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