Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition

Authors:
M. Hinze;S. Volkwein
Affiliations:
Universität Hamburg, Department Mathematik, Schwerpunkt Approximation and Optimierung, Geomatikum, Hamburg, Germany;Karl-Franzens-Universität Graz, Institut für Mathematik and Wissenschaftliches Rechnen, Graz, Austria
Venue:
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Year:
2008

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Abstract

In this paper we investigate POD discretizations of abstract linear-quadratic optimal control problems with control constraints. We apply the discrete technique developed by Hinze (Comput. Optim. Appl. 30:45-61, 2005) and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the adjoint system from Kunisch and Volkwein (Numer. Math. 90:117-148, 2001; SIAM J. Numer. Anal. 40:492-515, 2002). Finally, we present numerical examples that illustrate the theoretical results.