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In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimality conditions are derived for the regularized problems as well. It is further shown that these conditions are also sufficient for superlinear convergence of the semi-smooth Newton algorithm to be well-defined and superlinearly convergent when applied to the first order optimality system associated with the regularized problems.
@article{COCV_2012__18_2_520_0,
author = {Kunisch, Karl and Wachsmuth, Daniel},
title = {Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {520--547},
publisher = {EDP-Sciences},
volume = {18},
number = {2},
year = {2012},
doi = {10.1051/cocv/2011105},
mrnumber = {2954637},
zbl = {1246.49021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011105/}
}
TY - JOUR AU - Kunisch, Karl AU - Wachsmuth, Daniel TI - Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 520 EP - 547 VL - 18 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011105/ DO - 10.1051/cocv/2011105 LA - en ID - COCV_2012__18_2_520_0 ER -
%0 Journal Article %A Kunisch, Karl %A Wachsmuth, Daniel %T Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 520-547 %V 18 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011105/ %R 10.1051/cocv/2011105 %G en %F COCV_2012__18_2_520_0
Kunisch, Karl; Wachsmuth, Daniel. Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 520-547. doi : 10.1051/cocv/2011105. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011105/
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