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We focus our discussion on gradient based methods for constrained optimization
problems.
The expensive part in such methods
is the equation solver per
each optimization step (and in addition to this the solver for the
adjoint equation in the adjoint method).
Although these equations may be solved only approximately, still they consist
the major part of the solution time.
Multigrid methods can be used in a variety of ways to accelerate gradient
based optimizers.
We distinguish between multigrid methods that are used for the acceleration of
a step in some optimization procedure to genuinely multigrid
methods that aim at the full optimization problem.

**Subsections**

Shlomo Ta'asan
2001-08-22