Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
SIAM Journal on Control and Optimization
A space-time multigrid method for parabolic partial differential equations
SIAM Journal on Scientific Computing
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Multigrid
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Asymptotic Properties of Receding Horizon Optimal Control Problems
SIAM Journal on Control and Optimization
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Multigrid methods for parabolic distributed optimal control problems
Journal of Computational and Applied Mathematics
Semismooth Newton and Augmented Lagrangian Methods for a Simplified Friction Problem
SIAM Journal on Optimization
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
A Multigrid Scheme for Elliptic Constrained Optimal Control Problems
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Real-Time PDE-Constrained Optimization (Computational Science and Engineering)
Real-Time PDE-Constrained Optimization (Computational Science and Engineering)
Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Multigrid Methods for PDE Optimization
SIAM Review
SIAM Journal on Scientific Computing
Computational Optimization and Applications
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A mesh-independent and second-order accurate multigrid strategy to solve control-constrained parabolic optimal control problems is presented. The resulting algorithms appear to be robust with respect to change of values of the control parameters and have the ability to accommodate constraints on the control also in the limit case of bang-bang control. Central to the development of these multigrid schemes is the design of iterative smoothers which can be formulated as local semismooth Newton methods. The design of distributed controls is considered to drive nonlinear parabolic models to follow optimally a given trajectory or attain a final configuration. In both cases, results of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed schemes are able to solve parabolic optimality systems with textbook multigrid efficiency. Further results are presented to validate second-order accuracy and the possibility to track a trajectory over long time intervals by means of a receding-horizon approach.