James V. Burke

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Let f be a continuous function on Rn, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which f is not differentiable. Of particular interest is the case where f is not convex, and perhaps not even locally Lipschitz, but is a function whose gradient is(More)
H∞ controller design for linear systems is a difficult, nonconvex and typically nonsmooth (nondifferentiable) optimization problem when the order of the controller is fixed to be less than that of the open-loop plant, a typical requirement in e.g. embedded aerospace control systems. In this paper we describe a new matlab package called hifoo, aimed at(More)
A non{interior path following algorithm is proposed for the linear complementarity problem. The method employs smoothing techniques introduced by Kanzow. If the LCP is P 0 +R 0 and satisses a non{degeneracy condition due to Fukushima, Luo, and Pang, then the algorithm is globally linearly convergent. As with interior point path following methods, the(More)
Stabilization by static output feedback (SOF) is a long-standing open problem in control: given an n by n matrix A and rectangular matrices B and C, find a p by q matrix K such that A + BKC is stable. Low-order controller design is a practically important problem that can be cast in the same framework, with (p+k)(q+k) design parameters instead of pq, where(More)
An extension of the Gauss{Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h F under two conditions, namely h has a set of weak sharp minima, C, and there is a regular point of the inclusion F(x) 2 C. This result extends a similar convergence(More)
Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in(More)
Many interesting real functions on Euclidean space are differentiable almost everywhere. All Lipschitz functions have this property, but so, for example, does the spectral abscissa of a matrix (a non-Lipschitz function). In practice, the gradient is often easy to compute. We investigate to what extent we can approximate the Clarke subdifferential of such a(More)