4 A Multigrid Method for the Solution of Linear-Quadratic Optimal Control Problems
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چکیده
The main part of this chapter is devoted to the development and presentation of a coupled multigrid method for the solution of saddle point systems (2.51) arising from the discretization of PDE constrained optimization problems. In subsequent chapters, the devised method will be adapted to handle inequality constraints on the control, and it will be employed for the solution of the systems, which are generated when applying Newton-type methods to optimization problems with nonlinear constraints. The multigrid method is one of the most efficient solution methods for linear systems arising from discretized second-order elliptic boundary value problems. The algebraic error usually satisfies an estimate of the form
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