Kurdyka-Lojasiewicz – Optimization Online

A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition

Published: 2026/08/05

Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming convergence rates, Kurdyka-Lojasiewicz, nonconvex optimization, proximal subgradient, stochastic approximation methods, stochastic programming

This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more

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