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Minimal invasion: An optimal L∞ state constraint problem
Published online by Cambridge University Press: 11 October 2010
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.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 3 , May 2011 , pp. 505 - 522
- Copyright
- © EDP Sciences, SMAI, 2010
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