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arXiv · 1607.00809

Optimal control of a rate-independent evolution equation via viscous regularization

Ulisse Stefanelli·Gerd Wachsmuth·Daniel Wachsmuth
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Abstract

We study the optimal control of a rate-independent system that is driven by a convex, quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality conditions, we study the regularization of the problem via a smoothing of the dissipation potential and via the addition of some viscosity. The resulting regularized optimal control problem is analyzed. By driving the regularization parameter to zero, we obtain a necessary optimality condition for the original, non-smooth problem.

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Ulisse Stefanelli, Gerd Wachsmuth, Daniel Wachsmuth. 2016-07-04. Optimal control of a rate-independent evolution equation via viscous regularization. https://arxiv.org/abs/1607.00809

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