Numerical methods for Nash equilibria in multiobjective control of partial differential equations



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Ramos del Olmo, Ángel Manuel (2003) Numerical methods for Nash equilibria in multiobjective control of partial differential equations. In Analysis and optimization of differential systems : IFIP TC7-WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10-14, 2002, Constanta, Romania. IFIP (121). Kluwer Academic Publishers, Boston, pp. 333-344. ISBN 1-4020-7439-5

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This paper is concerned with the numerical solution of multiobjective control problems associated with linear (resp., nonlinear) partial differential equations. More precisely, for such problems, we look for Nash equilibria, which are solutions to noncooperative games. 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 (resp., a suitable algorithm) for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.

Item Type:Book Section
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Incluye colaboración de Luis Alberto Fernández Fernández y Cecilia Pola Méndez.

Uncontrolled Keywords:Partial diferential equations; Heat equation; Burgers equation; Optimal control; Pointwise control; Nash equilibria; Adjoint systems; Conjugate gradient methods; multiobjective optimization; Quasi-Newton algorithms.
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:17719
Deposited On:17 Jan 2013 09:45
Last Modified:12 Dec 2018 15:07

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