# Minimal invasion: An optimal L∞ state constraint problem

Christian Clason; Kazufumi Ito; Karl Kunisch

- Volume: 45, Issue: 3, page 505-522
- ISSN: 0764-583X

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topClason, Christian, Ito, Kazufumi, and Kunisch, Karl. "Minimal invasion: An optimal L∞ state constraint problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.3 (2011): 505-522. <http://eudml.org/doc/273284>.

@article{Clason2011,

abstract = {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.},

author = {Clason, Christian, Ito, Kazufumi, Kunisch, Karl},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {optimal control; optimal L∞ state constraint; semi-smooth Newton method; optimal state constraint; Moreau-Yosida regularization; superlinear convergence; numerical examples},

language = {eng},

number = {3},

pages = {505-522},

publisher = {EDP-Sciences},

title = {Minimal invasion: An optimal L∞ state constraint problem},

url = {http://eudml.org/doc/273284},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Clason, Christian

AU - Ito, Kazufumi

AU - Kunisch, Karl

TI - Minimal invasion: An optimal L∞ state constraint problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 3

SP - 505

EP - 522

AB - 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.

LA - eng

KW - optimal control; optimal L∞ state constraint; semi-smooth Newton method; optimal state constraint; Moreau-Yosida regularization; superlinear convergence; numerical examples

UR - http://eudml.org/doc/273284

ER -

## References

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- [8] G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems. The University Series in Mathematics, Plenum Press, New York (1987). Zbl0655.35002MR1094820

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