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

  • Mohammad Tanvir Rahman (a1) and Alfio Borzì (a1)
Abstract
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.

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*Email addresses: tanvir.rahman@mathematik.uni-wuerzburg.de (Mohammad Tanvir Rahman), alfio.borzi@mathematik.uni-wuerzburg.de, (Alfio Borzí)
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] A. Borzì and C. Kanzow , Formulation and numerical solution of nash equilibrium multiobjective elliptic control problems, SIAM J. Control Optim., 51(2013), 718744.

[3] A. Borzì and K. Kunisch , A multigrid scheme for elliptic constrained optimal control problems, Comput. Optim. Appl., 31 (2005), pp. 309333.

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[9] J.-A. Désidéri , Cooperation and competition in multidisciplinary optimization. Application to the aero-structural aircraft wing shape optimization. Comput. Optim. Appl., 52 (2012), pp. 2968.

[13] G.P. Liu , J.B. Yang , and J.F. Whidborne , Multiobjective Optimisation and Control, Research Studies Press LTD, 2001.

[16] A. Rösch , Error estimates for linear-quadratic control problems with control constraints, Optimization Methods and Software 21 (2006), 121134.

[17] W. Stadler , Fundamentals of multicriteria optimization, In Multicriteria optimization in engineering and in the sciences, volume 37 of Math. Concepts Methods Sci. Engrg., pages 125. Plenum, New York, 1988.

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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
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