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Nash equilibria for the multiobjective control of linear partial differential equations

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Ramos del Olmo, Ángel Manuel and Glowinski, R. and Periaux, J. (2002) Nash equilibria for the multiobjective control of linear partial differential equations. Journal of optimization theory and applications, 112 (2). pp. 457-498. ISSN 0022-3239

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Official URL: http://link.springer.com/content/pdf/10.1023%2FA%3A1017981514093


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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.


Item Type:Article
Uncontrolled Keywords:Linear partial differential equations, optimal control; Nash equilibria; Adjoint systems; conjugate-gradient methods; Multiobjective optimization.
Subjects:Sciences > Mathematics > Operations research
ID Code:17712
Deposited On:16 Jan 2013 11:38
Last Modified:12 Dec 2018 15:07

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