Multigrid Optimization Methods for the Optimal Control of Convection–Diffusion Problems with Bilinear Control

A. Borzì (), E.-J. Park () and M. Vallejos Lass ()
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A. Borzì: Universität Würzburg, Emil-Fischer-Straße 30
E.-J. Park: Yonsei University
M. Vallejos Lass: University of the Philippines

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 7, 510-533

Abstract: Abstract Optimal control problems, governed by convection–diffusion equations with bilinear control, are studied. For the realization of the numerical solution, the multigrid for optimization method together with finite difference discretization is utilized and investigated. In addition, the extension to constrained optimal control problems with bilinear control is considered. Results of numerical experiments show the computational performance of the proposed multigrid scheme in solving optimal control problems subject to a convection–diffusion equation with bilinear control. We obtain that the proposed multigrid strategy accelerates classical one-grid optimization schemes and inherits the order of convergence of the finite difference discretization. Moreover, the mesh independence principle is obtained, which is a typical characterization of a multigrid strategy.

Keywords: Optimal control; Multigrid methods; Convection–diffusion; Bilinear control; Finite differences; 49J20; 49K20; 65N06; 65N55 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-015-0791-z

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