single-loop scheme – Optimization Online

Projection-Free Algorithms for Nonsmooth Stochastic Convex-Concave Saddle-Point Problems

Published: 2026/09/30

We study nonsmooth convex-concave saddle-point problems over compact convex sets, assuming access to stochastic subgradients of the payoff function. We develop single-loop projection-free algorithms that use linear minimization oracles over the primal and dual domains. Unlike prior projection-free approaches that rely on smoothing, our methods are purely subgradient-based and handle nonsmoothness directly. This design makes … Read more

First-order methods for stochastic and finite-sum convex optimization with deterministic constraints

Published: 2025/06/25

Constrained Nonlinear Optimization, Convex Optimization, Stochastic Programming accelerated gradient, finite-sum optimization, quadratic penalty, sample average approximation, single-loop scheme, stochastic optimization, variance reduction

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an \(\epsilon\)-expectedly feasible stochastic optimal solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance ϵ. However, in many practical applications, constraints must be nearly … Read more