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Stadler, Georg

Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices. (English) Zbl 1185.49031

Comput. Optim. Appl. 44, No. 2, 159-181 (2009).
Summary: Elliptic optimal control problems with \(L^1\)-control cost are analyzed. Due to the nonsmooth objective functional the optimal controls are identically zero on large parts of the control domain. For applications, in which one cannot put control devices (or actuators) all over the control domain, this provides information about where it is most efficient to put them. We analyze structural properties of \(L^1\)-control cost solutions. For solving the non-differentiable optimal control problem we propose a semismooth Newton method that can be stated and analyzed in function space and converges locally with a superlinear rate. Numerical tests on model problems show the usefulness of the approach for the location of control devices and the efficiency of our algorithm.

Cited in 1 Review
Cited in 130 Documents

MSC:

49M15 Newton-type methods
49N60 Regularity of solutions in optimal control

Keywords:

optimal control; nonsmooth regularization; optimal actuator location; placement of control devices; semismooth Newton; active set method
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References:

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