Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 17, Issue 3, Pages 858-886Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1051/cocv/2010027
Keywords
Non-smooth optimization; sparsity; regularization error estimates; finite elements; discretization error estimates
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Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L(1)-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.
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