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Pointwise control of the Burgers equation and related Nash equilibrium problems: Computational approach

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Ramos del Olmo, Ángel Manuel and Glowinski, R. and Periaux, J. (2002) Pointwise control of the Burgers equation and related Nash equilibrium problems: Computational approach. Journal of optimization theory and applications, 112 (3). pp. 499-516. ISSN 0022-3239

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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.


Item Type:Article
Uncontrolled Keywords:Burgers equation, pointwise control; Nash equilibria;Adjoint system; Dirac measures; quasi-Newton algorithms; Singleobjective control problems; multiobjective control problems.
Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Operations research
ID Code:17723
Deposited On:17 Jan 2013 09:43
Last Modified:12 Dec 2018 15:07

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