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A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems

Published online by Cambridge University Press:  28 May 2015

Mohammad Tanvir Rahman  and
Alfio Borzì
Mohammad Tanvir Rahman
Affiliation:
Department of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
Alfio Borzì*
Affiliation:
Department of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
*
*Email addresses: [email protected] (Mohammad Tanvir Rahman), [email protected], (Alfio Borzí)
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Abstract

A finite-element multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The multigrid computational framework implements a nonlinear multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the multigrid scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.

Keywords

15A1265F1065F15Elliptic partial differential equationsmultigrid methodsNash equilibriumoptimal control theoryfinite element method
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 2 , May 2015 , pp. 253 - 282
Copyright
Copyright © Global-Science Press 2015 

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