stochastic approximation methods – 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

Stochastic first order methods in smooth convex optimization.

Published: 2012/01/19

Olivier Devolder

Convex Optimization, Stochastic Programming complexity, fast gradient method, first-order methods, probability of large deviations, smooth convex optimization, stochastic approximation methods, stochastic optimization

In this paper, we are interested in the development of efficient first-order methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the first-order information. First, we consider the Stochastic Primal Gradient method, which is nothing else but the Mirror Descent SA method applied to a smooth … Read more