In this chapter we present the principles of the space-mapping iteration techniques
for the efficient solution of optimization problems. We also show how space-mapping optimization
can be understood in the framework of defect correction.
We observe the difference between the solution of the optimization problem and the computed
space-mapping solutions. We repair this discrepancy by exploiting the correspondence
with defect correction iteration and we construct the manifold-mapping algorithm, which is as
efficient as the space-mapping algorithm but converges to the true solution.
In the last section we show a simple example from practice, comparing space-mapping
and manifold mapping and illustrating the efficiency of the technique
