Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations |
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Authors: | Ramos AM Glowinski R Periaux J |
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Institution: | (1) Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain;(2) Laboratoire d'Analyse Numérique, Université P. et M. Curie, Paris, France;(3) Department of Mathematics, University of Houston, Houston, Texas;(4) Dassault Aviation, Saint Cloud, France |
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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. |
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Keywords: | Linear partial differential equations optimal control Nash equilibria adjoint systems conjugate-gradient methods multi-objective optimization |
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