Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior of the new method is demonstrated and a comparison to classical continuation methods is provided.

Keywords: extrapolation, mixed control-state constraints, PDE-constrained optimization, semismooth Newton algorithm, sensitivity, state constraints

@article{COCV_2010__16_3_503_0, author = {Hinterm\"uller, Michael and Yousept, Irwin}, title = {A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {503--522}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, doi = {10.1051/cocv/2009016}, mrnumber = {2674624}, zbl = {1201.49032}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009016/} }

TY - JOUR AU - Hintermüller, Michael AU - Yousept, Irwin TI - A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 503 EP - 522 VL - 16 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009016/ DO - 10.1051/cocv/2009016 LA - en ID - COCV_2010__16_3_503_0 ER -

%0 Journal Article %A Hintermüller, Michael %A Yousept, Irwin %T A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 503-522 %V 16 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009016/ %R 10.1051/cocv/2009016 %G en %F COCV_2010__16_3_503_0

Hintermüller, Michael; Yousept, Irwin. A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 503-522. doi : 10.1051/cocv/2009016. http://archive.numdam.org/articles/10.1051/cocv/2009016/

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