Convergence and regularization results for optimal control problems with sparsity functional

• Published in: ESAIM. Control, optimisation and calculus of variations Vol. 17; no. 3; pp. 858 - 886
• Main Authors: Wachsmuth, Gerd, Wachsmuth, Daniel
• Format: Journal Article
• Language: English
• 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

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...