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

  • * Corresponding author: D. Wachsmuth.

    * Corresponding author: D. Wachsmuth. 
The second and third author were supported by DFG grants within the Priority Program SPP 1962 (Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization), which is gratefully acknowledged.
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  • 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.

    Mathematics Subject Classification: Primary: 49K20; Secondary: 35K87.

    Citation:

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