Minimal invasion: An optimal ${L}^{\infty }$ state constraint problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, p. 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 : https://doi.org/10.1051/m2an/2010064
Classification:  49J52,  49J20,  49K20
Keywords: optimal control, optimal L∞ state constraint, semi-smooth Newton method
@article{M2AN_2011__45_3_505_0,
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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
pages = {505-522},
doi = {10.1051/m2an/2010064},
zbl = {1269.65060},
language = {en},
url = {http://www.numdam.org/item/M2AN_2011__45_3_505_0}
}

Clason, Christian; Ito, Kazufumi; Kunisch, Karl. Minimal invasion: An optimal $L^\infty$ state constraint problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, pp. 505-522. doi : 10.1051/m2an/2010064. http://www.numdam.org/item/M2AN_2011__45_3_505_0/

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