Liwei Jiang – Optimization Online

A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth

Published: 2022/04/29, Updated: 2022/05/04

Convex and Nonsmooth Optimization active manifold, decomposable, Goldstein, Kurdyka-Lojasiewicz, max-of-smooth, nonsmooth, parameter-free, quadratic growth, semialgebraic, subgradient method

Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linearly convergent method for nonsmooth functions with quadratic growth. This work designs such a method for a wide class of nonsmooth and nonconvex locally Lipschitz functions, including max-of-smooth, Shapiro’s decomposable … Read more

Subgradient methods near active manifolds: saddle point avoidance, local convergence, and asymptotic normality

Published: 2021/08/25, Updated: 2021/08/26

Damek Davis

Dmitriy Drusvyatskiy

Liwei Jiang

Nonsmooth Optimization

Nonsmooth optimization problems arising in practice, whether in signal processing, statistical estimation, or modern machine learning, tend to exhibit beneficial smooth substructure: their domains stratify into “active manifolds” of smooth variation, which common proximal algorithms “identify” in finite time. Identification then entails a transition to smooth dynamics, and permits the use of second-order information for … Read more