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Active set strategy for constrained optimal control problems: The finite dimensional case. (English) Zbl 0978.49026
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 36-54 (2000).
Summary: We consider control constrained and state constrained optimal control problems governed by elliptic partial differential equations, once they have been discretized. We propose and analyze an algorithm for efficient solution of these finite-dimensional problems. It is based on an active set strategy involving primal as well as dual variables and is suggested by a generalized Moreau-Yosida regularization of the control (or state) constraint. Sufficient conditions for convergence in finitely many iterations are given. At last, we present numerical examples and discuss the role of the strict complementarity condition.
For the entire collection see [Zbl 0935.00054].
49M25 Discrete approximations in optimal control
49K20 Optimality conditions for problems involving partial differential equations
49M37 Numerical methods based on nonlinear programming