Rigorous quantitative analysis of multigrid, I: constant coefficients two-level cycle with L2-norm
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Primal-dual interior-point methods
Primal-dual interior-point methods
Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
SIAM Journal on Scientific Computing
Primal-Dual Strategy for Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Multigrid
Optimal Control of Distributed Systems: Theory and Applications
Optimal Control of Distributed Systems: Theory and Applications
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
An Algebraic Multigrid Method for a Class of Elliptic Differential Systems
SIAM Journal on Scientific Computing
Superconvergence Properties of Optimal Control Problems
SIAM Journal on Control and 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
SIAM Journal on Scientific Computing
Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
SIAM Journal on Scientific Computing
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We consider the fast and efficient numerical solution of linear-quadratic optimal control problems with additional constraints on the control. Discretization of the first-order conditions leads to an indefinite linear system of saddle point type with additional complementarity conditions due to the control constraints. The complementarity conditions are treated by a primal-dual active set strategy that serves as outer iteration. At each iteration step, a KKT system has to be solved. Here, we develop a multigrid method for its fast solution. To this end, we use a smoother which is based on an inexact constraint preconditioner. We present numerical results which show that the proposed multigrid method possesses convergence rates of the same order as for the underlying (elliptic) PDE problem. Furthermore, when combined with a nested iteration, the solver is of optimal complexity and achieves the solution of the optimization problem at only a small multiple of the cost for the PDE solution.