Titelaufnahme

Titel
A convex analysis approach to optimal controls with switching structure for partial differential equations.
Verfasser/ VerfasserinClason, Christian ; Kazufumi, Ito ; Kunisch, Karl
Erschienen in
ESAIM: Control, Optimisation and Calculus of Variations, 2016, Jg. 22, H. 2, S. 581-609
ErschienenEDP Sciences, 2016
Ausgabe
Accepted version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (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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A convex analysis approach to optimal controls with switching structure for partial differential equations. [1.06 mb]
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Zusammenfassung (Englisch)

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.