Accuracy and Convergence Properties of the Finite Difference Multigrid Solution of an Optimal Control Optimality System

Authors:
Alfio Borzì;Karl Kunisch;Do Y. Kwak
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2002

Citing 0
Cited 6

A Multigrid Scheme for Elliptic Constrained Optimal Control Problems

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High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems

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Conjugate gradient-boundary element solution using multiple reciprocity method for distributed elliptic optimal control problems

Applied Numerical Mathematics
Efficient Preconditioners for Optimality Systems Arising in Connection with Inverse Problems

SIAM Journal on Control and Optimization
A Robust Multigrid Method for Elliptic Optimal Control Problems

SIAM Journal on Numerical Analysis
A local Fourier convergence analysis of a multigrid method using symbolic computation

Journal of Symbolic Computation

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Abstract

The finite difference multigrid solution of an optimal control problem associated with an elliptic equation is considered. Stability of the finite difference optimality system and optimal-order error estimates in the discrete L2 norm and in the discrete H1 norm under minimum smoothness requirements on the exact solution are proved. Sharp convergence factor estimates of the two grid method for the optimality system are obtained by means of local Fourier analysis. A multigrid convergence theory is provided which guarantees convergence of the multigrid process towards weak solutions of the optimality system.