H /sup ∞/ Optimization and Semidefinite Programming
J. William Helton, Orlando Merino, Trent E. Walker · 2005
This article shows how the fundamental HOO optimiza tion problem of control can be naturally treated with modern primal-dual interior point (PDIP) methods. The fundamental H= problem of control is that of find ing 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 HOO 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 HOO problems, and com pare natural (PDIP) algorithms for these problems, as well as fit them into the context of classical lIDO theory. The method which we expect will be very effective on Hoo optimization problems might be thought of as a hy brid between primal-dual methods and those for tradi tional optimization of smooth objectives functions. For example, a simple Hoo optimization problem is, given g, find