  We present a successive constraint approach that makes it possible to cheaply
solve large-scale linear matrix inequalities for a large number of parameter
values. The efficiency of our method is made possible by an offline/online
decomposition of the workload. Expensive computations are performed beforehand,
in the offline stage, so that the problem can be solved very cheaply in the
online stage. We also extend the method to approximate solutions to
semidefinite programming problems.
