106 citations · 247 across the 34 of their papers we have counts for
37 papers
The complexity of first-order optimization methods from a metric perspective
Adrian S. Lewis, Tonghua Tian
A central tool for understanding first-order optimization algorithms is the Kurdyka-Lojasiewicz inequality. Standard approaches to such methods rely crucially on this inequality to…
Basic convex analysis in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however…
Identifiability, the KL property in metric spaces, and subgradient curves
Adrian Lewis, Tonghua Tian
Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorit…
Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimization
X. Y. Han, Adrian S. Lewis
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous non…
Local linear convergence of alternating projections in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, eq…
The structure of conservative gradient fields
Adrian Lewis, Tonghua Tian
The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized g…