Discretization and optimization techniques

The functions and are sufficiently smooth and are of appropriate dimension. The upper subscript denotes the dependence on the stepsize. The optimization variable will comprise both the discretized state and control variables.

The form (1) will be achieved by solving
the elliptic equation (2) resp. (26)
with the standard five-point-star discretization scheme.
Choose a number
and the stepsize
Consider the mesh points

and define the following sets of indices residing either in the domain or on the four edges of the boundary :

Obviously, we have ; define further .

We shall first discuss discretization schemes for the boundary control
problem and will then only indicate the necessary
modifications to obtain schemes for the distributed control problem.

- Discretization of the boundary control problem
- Discretization of the distributed control problem
- Optimization codes and modeling environment

2000-12-09