This article shows how the fundamental H
optimization
problem of control can be naturally treated with modern
primal-dual interior point (PDIP) methods.
The fundamental H problem of control
is that of finding the stable frequency response function
which best fits worst case frequency domain specifications.
This is a non smooth optimization problem which underlies
the frequency domain formulation of the H problem of
control;
it is the main optimization problem in QFT for example.
Also, in this article we present new
optimality conditions for matrix valued H problems,
and compare natural (PDIP) algorithms for these problems, as well
as fit them
into the context of classical H theory.
What we give in this article might be thought of as a hybrid
between primal-dual methods and those for traditional optimization
of smooth
objective functions. We give a theory which has generalizes both.
This contains as a special case the method (Indiana J 1994)
which we found to be very effective on H optimization
problems.
Also it generalizes certain aspects of
theory and methods now widely popular for solving
Linear Matrix Inequalities (LMI).
