Error estimates for the approximation of multibang control problems

Christian Clason (), Thi Bich Tram Do () and Frank Pörner ()
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Christian Clason: University Duisburg-Essen
Thi Bich Tram Do: University Duisburg-Essen
Frank Pörner: University of Würzburg

Computational Optimization and Applications, 2018, vol. 71, issue 3, No 10, 857-878

Abstract: Abstract This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional “multibang” regularization functional that promotes optimal control taking values from a given discrete set pointwise almost everywhere. Under a regularity condition on the set where these discrete values are attained, error estimates for the Moreau–Yosida approximation (which allows its solution by a semismooth Newton method) and the discretization of the problem are derived. Numerical results support the theoretical findings.

Keywords: Multibang control; Moreau-Yosida approximation; Finite element discretization; Error estimates; Semi-smooth Newton method (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-018-0026-y

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