Yifeng Xiao – Optimization Online

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

Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees

Published: 2024/09/15, Updated: 2024/10/10

Zhaosong Lu

Sanyou Mei

Yifeng Xiao

Constrained Nonlinear Optimization, Stochastic Programming Polyak momentum, quadratic penalty, recursive momentum, sample complexity, stochastic optimization, variance reduction

In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, … Read more