Primal-Dual Strategy for Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems
SIAM Journal on Optimization
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
The Primal-Dual Active Set Method for Nonlinear Optimal Control Problems with Bilateral Constraints
SIAM Journal on Control and Optimization
A Primal-Dual Active Set Algorithm for Three-Dimensional Contact Problems with Coulomb Friction
SIAM Journal on Scientific Computing
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Multigrid Algorithms for Inverse Problems with Linear Parabolic PDE Constraints
SIAM Journal on Scientific Computing
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Multigrid Methods for PDE Optimization
SIAM Review
Computational Optimization and Applications
IEEE Transactions on Information Theory
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We study optimal control problems in which controls with certain sparsity patterns are preferred. For time-dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval. The approach uses a nondifferentiable cost functional to implement the sparsity requirements; additionally, bound constraints for the optimal controls can be included. We study the resulting problem in appropriate function spaces and present two solution methods of Newton type, based on different formulations of the optimality system. Using elliptic and parabolic test problems we research the sparsity properties of the optimal controls and analyze the behavior of the proposed solution algorithms.