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- Adrian S. Lewis, Gregory P. Knowles
- IEEE Trans. Image Processing
- 1992

The 2-D orthogonal wavelet transform decomposes images into both spatial and spectrally local coefficients. The transformed coefficients were coded hierarchically and individually quantized in… (More)

- 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… (More)

- D. Leventhal, Adrian S. Lewis
- Math. Oper. Res.
- 2010

- Adrian S. Lewis, Michael L. Overton
- Math. Program.
- 2013

We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search that generates a sequence of nested… (More)

Given a real-analytic function f : Rn → R and a critical point a ∈ Rn, the Lojasiewicz inequality asserts that there exists θ ∈ [ 1 2 , 1) such that the function |f − f(a)|θ ‖∇f‖−1 remains bounded… (More)

- Jonathan M. Borwein, Adrian S. Lewis
- Math. Program.
- 1992

In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint… (More)

- Jonathan M. Borwein, Adrian S. Lewis
- Math. Program.
- 1992

We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the… (More)

- Adrian S. Lewis
- SIAM Journal on Optimization
- 1996

There is growing interest in optimization problems with real symmetric matrices as variables. Generally the matrix functions involved are spectral: they depend only on the eigenvalues of the matrix.… (More)

- Adrian S. Lewis, D. R. Luke, Jérôme Malick
- Foundations of Computational Mathematics
- 2009

The idea of a finite collection of closed sets having “linearly regular intersection” at a point is crucial in variational analysis. This central theoretical condition also has striking algorithmic… (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… (More)