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Abstract In this paper we develop an augmented Lagrangian method to determine local optimal solutions of the reduced‐ and fixed‐order H ∞ synthesis problems. We cast these synthesis problems as optimization programs with a linear cost subject to linear matrix inequality (LMI) constraints along with nonlinear equality constraints representing a matrix inversion condition. The special feature of our algorithm is that only equality constraints are included in the augmented Lagrangian, while LMI constraints are kept explicitly in order to exploit currently available semi definite programming (SDP) codes. The step computation in the tangent problem is based on a Gauss–Newton model, and a specific line search and a first‐order Lagrange multiplier update rule are used to enhance efficiency. A number of computational results are reported and underline the strong practical performance of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd.
Apkarian et al. (Thu,) studied this question.