106 citations · 247 across the 34 of their papers we have counts for
5 papers · 1 filter
Partial smoothness of the numerical radius at matrices whose fields of values are disks
Adrian S. Lewis, Michael L. Overton
Solutions to optimization problems involving the numerical radius often belong to a special class: the set of matrices having field of values a disk centered at the origin. After i…
Inexact alternating projections on nonconvex sets
Dmitriy Drusvyatskiy, Adrian S. Lewis
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a…
Partial smoothness and constant rank
Adrian S. Lewis, Jingwei Liang
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-orde…
Gradient Sampling Methods for Nonsmooth Optimization
James V. Burke, Frank E. Curtis, Adrian S. Lewis +2
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated an…
Rescaling nonsmooth optimization using BFGS and Shor updates
Jiayi Guo, Adrian S. Lewis
The BFGS quasi-Newton methodology, popular for smooth minimization, has also proved surprisingly effective in nonsmooth optimization. Through a variety of simple examples and compu…