Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI
SIAM Journal on Scientific and Statistical Computing
A space-time multigrid method for parabolic partial differential equations
SIAM Journal on Scientific Computing
Primal-Dual Strategy for Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Multigrid
The Numerical Solution of the Steady State Solid Fuel Ignition Model and Its Optimal Control
SIAM Journal on Scientific Computing
Asymptotic Properties of Receding Horizon Optimal Control Problems
SIAM Journal on Control and Optimization
A Multigrid Scheme for Elliptic Constrained Optimal Control Problems
Computational Optimization and Applications
Fast iterative solution of elliptic control problems in wavelet discretization
Journal of Computational and Applied Mathematics
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
Computational Optimization and Applications
SIAM Journal on Control and Optimization
Multigrid second-order accurate solution of parabolic control-constrained problems
Computational Optimization and Applications
SIAM Journal on Scientific Computing
A Fokker-Planck control framework for multidimensional stochastic processes
Journal of Computational and Applied Mathematics
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Multigrid schemes that solve parabolic distributed optimality systems discretized by finite differences are investigated. Accuracy properties of finite difference approximation are discussed and validated. Two multigrid methods are considered which are based on a robust relaxation technique and use two different coarsening strategies: semicoarsening and standard coarsening. The resulting multigrid algorithms show robustness with respect to changes of the value of v, the weight of the cost of the control, is sufficiently small. Fourier mode analysis is used to investigate the dependence of the linear twogrid convergence factor on v and on the discretization parameters. Results of numerical experiments are reported that demonstrate sharpness of Fourier analysis estimates. A multigrid algorithm that solves optimal control problems with box constraints on the control is considered.