Volume 8, Issue 2
A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems

Mohammad Tanvir Rahman & Alfio Borzì

Numer. Math. Theor. Meth. Appl.,8 (2015), pp. 253-282

Published online: 2015-08

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  • Abstract

p>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.

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@Article{NMTMA-8-253, author = {Mohammad Tanvir Rahman and Alfio Borzì}, title = {A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {2}, pages = {253--282}, abstract = {p>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.}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w11si}, url = {http://global-sci.org/intro/article_detail/nmtma/12410.html} }
TY - JOUR T1 - A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems AU - Mohammad Tanvir Rahman & Alfio Borzì JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 253 EP - 282 PY - 2015 DA - 2015/08 SN - 8 DO - http://dor.org/10.4208/nmtma.2015.w11si UR - https://global-sci.org/intro/article_detail/nmtma/12410.html KW - AB - p>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.
Mohammad Tanvir Rahman & Alfio Borzì. (1970). A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 8 (2). 253-282. doi:10.4208/nmtma.2015.w11si
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