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- W2076780919 abstract "We consider a system that is governed by a PDE of hyperbolic type, namely, the wave equation, and is controlled by a Dirichlet boundary control. For the penalization of terminal constraints, we compare the convergence of three penalization techniques: a differentiable penalty method, an exact penalization, and a smoothed exact penalization. The error of the solution of the differentiably penalized problem is at most of the order $1/sqrt{gamma}$, where $gamma$ is the penalty parameter. The exact penalization yields the exact solution if $gamma$ is sufficiently large. If $gamma$ is sufficiently large for the smoothed exact penalization, we obtain an error bound of the order $1/sqrt{beta}$, where $beta$ is the additional smoothing parameter. This method yields differentiable objective functions that remain uniformly strongly convex, since $gamma$ need not tend to infinity to obtain convergence. We also consider the penalization of distributed inequality state constraints that prescribe an upper bound for the $L^infty$-norm of the state. We prove the convergence with respect to the $L^2$-norm for a penalization of the constraint violation measured in the $L^1$-norm. We use this penalization technique to prove the existence of optimal controls for the inequality state constrained problem." @default.
- W2076780919 created "2016-06-24" @default.
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- W2076780919 date "2010-01-01" @default.
- W2076780919 modified "2023-09-26" @default.
- W2076780919 title "Penalty Techniques for State Constrained Optimal Control Problems with the Wave Equation" @default.
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- W2076780919 doi "https://doi.org/10.1137/080725921" @default.
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