Convergence and regularization results for optimal control problems with sparsity functional

Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates w...

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Published inESAIM. Control, optimisation and calculus of variations Vol. 17; no. 3; pp. 858 - 886
Main Authors Wachsmuth, Gerd, Wachsmuth, Daniel
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.07.2011
Subjects
49M05
49N45
65N15
65N30
Applied mathematics
Approximation
Control theory
discretization error estimates
Estimates
Finite element analysis
finite elements
Inverse problems
Non-smooth optimization
Numerical analysis
Optimization
regularization error estimates
Sparsity
Studies
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Summary:Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical experiments.
Bibliography:publisher-ID:cocv0968
PII:S1292811910000278
ark:/67375/80W-M4DLFDDG-V
istex:59EC908DF6536571DCF4B62F725C14B317605BEB
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2010027