Semi-smooth Newton methods for optimal control of the dynamical Lamé system with control constraints.

Axel Kröner 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : Optimal control problems governed by the dynamical Lamé system with additional constraints on the controls are analyzed. Different types of control action are considered: distributed, Neumann boundary and Dirichlet boundary control. To treat the inequality control constraints semi-smooth Newton methods are applied and their convergence is analyzed. Although semi-smooth Newton methods are widely studied in the context of PDE-constrained optimization little has been done in the context of the dynamical Lamé system. The novelty of the article is the proof that in case of distributed and Neumann boundary control the Newton method converges superlinearly. In case of Dirichlet control superlinear convergence is shown for a strongly damped Lamé system. The results are an extension of [A. Kröner , K. Kunisch , and B. Vexler ( 2011 ), SIAM J. Control Optim. 49 : 830 – 858], where optimal control problems of the classical wave equation are considered. The control problems are discretized by finite elements and numerical examples are presented.
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Contributor : Axel Kröner <>
Submitted on : Tuesday, October 18, 2016 - 1:10:10 PM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM

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Axel Kröner. Semi-smooth Newton methods for optimal control of the dynamical Lamé system with control constraints.. Numerical Functional Analysis and Optimization / Numerical Functional Analysis and Optimization An International Journal, 2013. ⟨hal-01383266⟩

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