Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
ESAIM: Control, Optimisation and Calculus of Variations, Volume 18 (2012) no. 2, p. 520-547

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.

DOI : https://doi.org/10.1051/cocv/2011105
Classification:  49K20,  47J20,  49M15
Keywords: variational inequalities, optimal control, sufficient optimality conditions, semi-smooth Newton method
@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},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {2},
     year = {2012},
     pages = {520-547},
     doi = {10.1051/cocv/2011105},
     zbl = {1246.49021},
     mrnumber = {2954637},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 18 (2012) no. 2, pp. 520-547. doi : 10.1051/cocv/2011105. http://www.numdam.org/item/COCV_2012__18_2_520_0/

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