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Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition. (English) Zbl 1191.49040
Summary: We investigate POD discretizations of abstract linear-quadratic optimal control problems with control constraints. We apply the discrete technique developed by M. Hinze [Comput. Optim. Appl. 30, No. 1, 45–61 (2005; Zbl 1074.65069)] and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the adjoint system from K. Kunisch and S. Volkwein [Numer. Math. 90, No. 1, 117–148 (2001; Zbl 1005.65112; SIAM J. Numer. Anal. 40, No. 2, 492–515 (2002; Zbl 1075.65118)]. Finally, we present numerical examples that illustrate the theoretical results.

MSC:
49N10 Linear-quadratic optimal control problems
49M25 Discrete approximations in optimal control
65K10 Numerical optimization and variational techniques
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