A globalization strategy for the multigrid solution of elliptic optimal control problems

A multigrid method for constrained optimal control problems

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 activeset strate...

Multigrid Methods for Elliptic Optimal Control Problems

Multigrid methods for elliptic optimal control problems

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

4 A Multigrid Method for the Solution of Linear-Quadratic Optimal Control Problems

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, whi...

B-Spline Solution of Boundary Value Problems of Fractional Order Based on Optimal Control Strategy

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...