Geodesic
A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 503-522

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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.

DOI : 10.1051/cocv/2009016
Classification : 49M15, 49M37, 65K05, 90C33
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://geodesic.mathdoc.fr/articles/10.1051/cocv/2009016/}
}
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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, Tome 16 (2010) no. 3, pp. 503-522. doi: 10.1051/cocv/2009016

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