no. 3
Minimal invasion: An optimal L ∞ state constraint problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 3, pp. 505-522

In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and well-posedness and superlinear convergence of the Newton method is shown. Numerical examples illustrate the features of this problem and the proposed approach.

DOI : 10.1051/m2an/2010064
Classification : 49J52, 49J20, 49K20
Keywords: optimal control, optimal L∞ state constraint, semi-smooth Newton method 
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     author = {Clason, Christian and Ito, Kazufumi and Kunisch, Karl},
     title = {Minimal invasion: {An} optimal $L^\infty $ state constraint problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {505--522},
     year = {2011},
     publisher = {EDP Sciences},
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     doi = {10.1051/m2an/2010064},
     zbl = {1269.65060},
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     url = {https://www.numdam.org/articles/10.1051/m2an/2010064/}
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Clason, Christian; Ito, Kazufumi; Kunisch, Karl. Minimal invasion: An optimal $L^\infty $ state constraint problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 3, pp. 505-522. doi: 10.1051/m2an/2010064

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