Posted Dec 1, 1995

H Optimization and Semidefinite Programming

By J. William Helton, Orlando Merino and Trent E. Walker

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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).

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