Exact Penalty Function for ℓ2, 1 Norm Minimization over the Stiefel Manifold. - Nachuan Xiao; Xin Liu 001; Ya-Xiang Yuan (SIAM J. Optim., 2021)

A class of smooth exact penalty function methods for optimization problems with orthogonality constraints. - Nachuan Xiao; Xin Liu 001; Ya-Xiang Yuan (Optim. Methods Softw., 2022)

Convergence Guarantees for Stochastic Subgradient Methods in Nonsmooth Nonconvex Optimization. - Nachuan Xiao; Xiaoyin Hu; Kim-Chuan Toh (CoRR, 2023)

An Improved Unconstrained Approach for Bilevel Optimization. - Xiaoyin Hu; Nachuan Xiao; Xin Liu 001; Kim-Chuan Toh (SIAM J. Optim., 2023)

Decentralized Stochastic Subgradient Methods for Nonsmooth Nonconvex Optimization. - Siyuan Zhang; Nachuan Xiao; Xin Liu 001 (CoRR, 2024)

Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization. - Nachuan Xiao; Kuangyu Ding; Xiaoyin Hu; Kim-Chuan Toh (CoRR, 2024)

A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints. - Lei Wang 224; Nachuan Xiao; Xin Liu 001 (CoRR, 2024)

Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees. - Nachuan Xiao; Xiaoyin Hu; Xin Liu 001; Kim-Chuan Toh (J. Mach. Learn. Res., 2024)

Dissolving Constraints for Riemannian Optimization. - Nachuan Xiao; Xin Liu 001; Kim-Chuan Toh (Math. Oper. Res., 2024)

A Riemannian Dimension-Reduced Second-Order Method with Application in Sensor Network Localization. - Tianyun Tang; Kim-Chuan Toh; Nachuan Xiao; Yinyu Ye 001 (SIAM J. Sci. Comput., 2024)

A Penalty-Free Infeasible Approach for a Class of Nonsmooth Optimization Problems Over the Stiefel Manifold. - Xin Liu 001; Nachuan Xiao; Yaxiang Yuan (J. Sci. Comput., 2024)

Adam-family Methods with Decoupled Weight Decay in Deep Learning. - Kuangyu Ding; Nachuan Xiao; Kim-Chuan Toh (Trans. Mach. Learn. Res., 2025)

Learning-Rate-Free Momentum SGD with Reshuffling Converges in Nonsmooth Nonconvex Optimization. - Xiaoyin Hu; Nachuan Xiao; Xin Liu 001; Kim-Chuan Toh (J. Sci. Comput., 2025)

CDOpt: a Python package for a class of Riemannian optimization. - Nachuan Xiao; Xiaoyin Hu; Xin Liu 001; Kim-Chuan Toh (Math. Program. Comput., 2025)