Geodesic
A minimum effort optimal control problem for elliptic PDEs
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 911-927

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This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation illustrate the behavior of minimum effort controls.

DOI : 10.1051/m2an/2011074
Classification : 49J52, 49J20, 49K20
Keywords: optimal control, minimum effort, L∞control cost, semi-smooth Newton method 
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     author = {Clason, Christian and Ito, Kazufumi and Kunisch, Karl},
     title = {A minimum effort optimal control problem for elliptic {PDEs}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {911--927},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {4},
     year = {2012},
     doi = {10.1051/m2an/2011074},
     mrnumber = {2891474},
     zbl = {1270.49023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011074/}
}
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Clason, Christian; Ito, Kazufumi; Kunisch, Karl. A minimum effort optimal control problem for elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 911-927. doi: 10.1051/m2an/2011074

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