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Title
A convex analysis approach to optimal controls with switching structure for partial differential equations.
AuthorClason, Christian ; Kazufumi, Ito ; Kunisch, Karl
Published in
ESAIM: Control, Optimisation and Calculus of Variations, 2016, Vol. 22, Issue 2, page 581-609
PublishedEDP Sciences, 2016
Edition
Accepted version
LanguageEnglish
Document typeJournal Article
Keywords (EN)Optimal control / switching control / partial differential equations / nonsmooth optimization / convexification / semi-smooth Newton method
ISSN1262-3377
URNurn:nbn:at:at-ubg:3-3462 Persistent Identifier (URN)
DOI10.1051/cocv/2015017 
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 The work is publicly available
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Abstract (English)

Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose MoreauYosida regularization is amenable to a semismooth Newton method in function space. This approach is especially suited for computing switching controls for partial differential equations. In this case, the optimality gap between the original functional and its relaxation can be estimated and shown to be zero for controls with switching structure. Numerical examples illustrate the effectiveness of this approach.

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