Nash equilibria for the multiobjective control of linear partial differential equations

  • Authors:

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

  • Affiliations:

  • Assistant Professor, Departamento de Matemá/tica Aplicada, Universidad Complutense de Madrid, Madrid, Spain;Professor, Laboratoire d'Analyse Numé/rique, Université/ P. et M. Curie, Paris, France/ Professor, Department of Mathematics, University of Houston, Houston, Texas;Chairman of the Scientific Pô/le, Dassault Aviation, Saint Cloud, France

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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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.