Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations

A.M. Ramos, R. Glowinski and J. Periaux
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A.M. Ramos: Universidad Complutense de Madrid
R. Glowinski: Université P. et M. Curie
J. Periaux: Dassault Aviation

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 3, No 1, 457-498

Abstract: 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.

Keywords: Linear partial differential equations; optimal control; Nash equilibria; adjoint systems; conjugate-gradient methods; multi-objective optimization (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1017981514093

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