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

The main result presented here gives the first order (necessary) conditions for solutions to /spl Hscr//sup /spl infin// optimization problems where there is an uncertainty parameter. These conditions can be stated as a set of equations which when solved produce excellent candidates for solutions, thus our result should lead to concrete algorithms in the spirit of the highly successful ones found by the authors for the certain plant case. How one crafts such algorithms for this uncertain case is indicated, but not analysed or tested. >

The main result presented here gives the first order (necessary) conditions for solutions to ℋ∞ optimization problems where there is an uncertainty parameter. These conditions can be stated as a set of equations which when solved produce excellent candidates for solutions, thus our result should lead to concrete algorithms in the spirit of the highly successful ones found by the authors for the certain plant case. How one crafts such algorithms for this uncertain case is indicated, but not analysed or tested

The fundamental H∞ optimization problem of control has become fairly well understood at both the qualitative and computational level. In many mature optimization theories one has a characterization of an optimizer which is a set of equations the optimizer must satisfy. Solution of these equations (say by Newton's method) then gives the optimizer. The trick is getting optimality equations which are nondegenerate with respect to Newton's method. This was done for pure H∞ optimization in previous papers by the authors, and in this article they extend the theory to include time domain constraints. Also an algorithm is described, a numerical example is presented, and a method for solving control problems is outlined

The fundamental H/sup /spl infin// optimization problem of control has become fairly well understood at both the qualitative and computational level. In many mature optimization theories one has a characterization of an optimizer which is a set of equations the optimizer must satisfy. Solution of these equations (say by Newton's method) then gives the optimizer. The trick is getting optimality equations which are nondegenerate with respect to Newton's method. This was done for pure H/sup /spl infin// optimization in previous papers by the authors, and in this article they extend the theory to include time domain constraints. Also an algorithm is described, a numerical example is presented, and a method for solving control problems is outlined.<>

A numerical algorithm for solving a fundamental optimisation problem, OPT∞, is presented. It is second-order convergent and performs very well in numerical experiments. The algorithm is based directly on the theoretical optimality conditions for OPT∞. An effective way to apply Newton's method to these conditions was found. This produces a tight theory which goes immediately from qualitative properties a designer would want to know to algorithms