Global minima for optimal control of the obstacle problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 64.

An optimal control problem subject to an elliptic obstacle problem is studied. We obtain a numerical approximation of this problem by discretising the PDE obtained via a Moreau–Yosida type penalisation. For the resulting discrete control problem we provide a condition that allows to decide whether a solution of the necessary first order conditions is a global minimum. In addition we show that the corresponding result can be transferred to the limit problem provided that the above condition holds uniformly in the penalisation and discretisation parameters. Numerical examples with unique global solutions are presented.

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DOI : 10.1051/cocv/2019039
Classification : 49J20, 49M05, 49M20, 65M15, 65M60
Mots-clés : Optimal control, obstacle problem, Moreau–Yosida penalisation, finite elements, global solution 
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     author = {Ali, Ahmad Ahmad and Deckelnick, Klaus and Hinze, Michael},
     title = {Global minima for optimal control of the obstacle problem},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2019039},
     mrnumber = {4150227},
     zbl = {1448.49004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2019039/}
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Ali, Ahmad Ahmad; Deckelnick, Klaus; Hinze, Michael. Global minima for optimal control of the obstacle problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 64. doi : 10.1051/cocv/2019039. http://www.numdam.org/articles/10.1051/cocv/2019039/

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