Shiji Zuo – Optimization Online

Curvature-oriented variance reduction methods for nonconvex stochastic optimization

Published: 2026/02/13, Updated: 2026/02/14

Constrained Nonlinear Optimization, Nonlinear Optimization cubic regularization, negative curvature direction, nonconvex constrained optimization, sample complexity, second-order stationarity

When pursuing an approximate second-order stationary point in nonconvex constrained stochastic optimization, is it possible to design a stochastic second-order method that achieves the same sample complexity order as in the unconstrained setting? To address this question in this paper, we first introduce Carme, a curvature-oriented variance reduction method designed for unconstrained nonconvex stochastic optimization. … Read more

An adaptive single-loop stochastic penalty method for nonconvex constrained stochastic optimization

Published: 2025/04/30, Updated: 2025/05/01

Shiji Zuo

Xiao Wang

Hao Wang

Constrained Nonlinear Optimization, Nonlinear Optimization

Adaptive update schemes for penalty parameters are crucial to enhancing robustness and practical applicability of penalty methods for constrained optimization. However, in the context of general constrained stochastic optimization, additional challenges arise due to the randomness introduced by adaptive penalty parameters. To address these challenges, we propose an Adaptive Single-loop Stochastic Penalty method (AdaSSP) in … Read more