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- James V. Burke, Adrian S. Lewis, Michael L. Overton
- SIAM Journal on Optimization
- 2005

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 isâ€¦ (More)

Hâˆž 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 atâ€¦ (More)

- James V. Burke, Shih-Ping Han
- Math. Program.
- 1989

- James V. Burke, Song Xu
- Math. Oper. Res.
- 1998

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, theâ€¦ (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, whereâ€¦ (More)

- James V. Burke, Michael C. Ferris
- Math. Program.
- 1995

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 convergenceâ€¦ (More)

- James V. Burke, Didier Henrion, Adrian S. Lewis, Michael L. Overton
- IEEE Transactions on Automatic Control
- 2006

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 inâ€¦ (More)

- James V. Burke
- 2002

A dynamical system áº‹ = Ax is robustly stable when all eigenvalues of complex matrices within a given distance of the square matrix A lie in the left half-plane. The â€˜pseudospectral abscissaâ€™, which is the largest real part of such an eigenvalue, measures the robust stability of A. We present an algorithm for computing the pseudospectral abscissa, proveâ€¦ (More)

- James V. Burke, Adrian S. Lewis, Michael L. Overton
- Math. Oper. Res.
- 2002

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 aâ€¦ (More)

- James V. Burke
- Math. Program.
- 1985