Geodesic
Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 626-652

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Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and comparing the efficiency of the proposed preconditioners.

DOI : 10.1051/cocv:2008042
Classification : 49K20, 65K05
Keywords: bilateral control-state constraints, heat equation, mesh independence, optimal control, PDE-constrained optimization, semismooth Newton method 
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     author = {Hinterm\"uller, Michael and Kopacka, Ian and Volkwein, Stefan},
     title = {Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {626--652},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {3},
     year = {2009},
     doi = {10.1051/cocv:2008042},
     mrnumber = {2542576},
     zbl = {1167.49027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008042/}
}
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Hintermüller, Michael; Kopacka, Ian; Volkwein, Stefan. Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 626-652. doi: 10.1051/cocv:2008042

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