Papers

---

Google Scholar

Preprints

---

• A single-loop regularized Newton method for nonconvex-strongly-concave minimax optimization
  Bohao Ma, Nachuan Xiao, Junyu Zhang
  arXiv preprint arXiv:2606.07003.
  

• Exact quadratic penalty function for symplectic eigenvalue problem
  Jiaqi Wang, Nachuan Xiao, Xin Liu*
  arXiv preprint arXiv:2604.19229.
  

• Line-search and adaptive step sizes for nonconvex-strongly-concave minimax optimization
  Bohao Ma, Nachuan Xiao*, Junyu Zhang
  arXiv preprint arXiv:2601.10086.
  

• A quadratically convergent alternating projection method for nonconvex sets
  Nachuan Xiao, Shiwei Wang*, Tianyun Tang, Kim-Chuan Toh
  arXiv preprint arXiv:2511.22916.
  

• Partial envelope for optimization problem with nonconvex constraints
  Xiaoyin Hu, Xin Liu, Kim-Chuan Toh, Nachuan Xiao*
  arXiv preprint arXiv:2510.22223.
  

• A hybrid subgradient method for nonsmooth nonconvex bilevel optimization
  Nachuan Xiao, Xiaoyin Hu*, Xin Liu, Kim-Chuan Toh
  arXiv preprint arXiv:2505.22040.
  

• A double tracking method for optimization with decentralized generalized orthogonality constraints
  Lei Wang, Nachuan Xiao, Xin Liu*
  arXiv preprint arXiv:2409.04998.
  

• A partial exact penalty function approach for constrained optimization
  Nachuan Xiao, Xin Liu*, Kim-Chuan Toh
  arXiv preprint arXiv:2304.01467.
  

Publications

---

^*: corresponding author

• AI for science: Progress, challenges, and perspectives
  Yongjun Xu, Zezhi Shao, Xin Liu, ..., Nachuan Xiao, et al.
  The Innovation, 2026, 101530 (in press).
  

• Stochastic subgradient methods with guaranteed global stability in nonsmooth nonconvex optimization
  Nachuan Xiao, Xiaoyin Hu*, Kim-Chuan Toh
  Mathematical Programming, 2026 (published online). arXiv
  

• An exact penalty approach for equality constrained optimization over a convex set
  Nachuan Xiao, Tianyun Tang, Shiwei Wang*, Kim-Chuan Toh
  Mathematical Programming, 2026 (published online). arXiv
  

• A minimization approach for minimax optimization with coupled constraints
  Xiaoyin Hu, Kim-Chuan Toh, Shiwei Wang, Nachuan Xiao*
  SIAM Journal on Optimization, 2026, 36(2): 811-840. arXiv
  

• Convergence of decentralized stochastic subgradient-based methods for nonsmooth nonconvex optimization
  Siyuan Zhang, Nachuan Xiao, Xin Liu*
  Journal of Machine Learning Research, 2026, 27(109): 1-52. arXiv
  

• Developing Lagrangian-based methods for nonsmooth nonconvex optimization
  Nachuan Xiao, Kuangyu Ding*, Xiaoyin Hu, Kim-Chuan Toh
  Mathematics of Operations Research, 2026 (Articles in Advance). arXiv
  

• An inexact preconditioned zeroth-order proximal method for composite optimization
  Shang-Lin Liu, Lei Wang*, Nachuan Xiao, Xin Liu
  Journal of the Operations Research Society of China, 2025 (published online). arXiv
  

• Adam-family methods with decoupled weight decay in deep learning
  Kuangyu Ding, Nachuan Xiao*, Kim-Chuan Toh
  Transactions on Machine Learning Research, 2025.
  

• Learning-rate-free momentum SGD with reshuffling converges in nonsmooth nonconvex optimization
  Xiaoyin Hu, Nachuan Xiao*, Xin Liu, Kim-Chuan Toh
  Journal of Scientific Computing, 2025, 102(3), Article 85. arXiv
  

• CDOpt: a Python package for a class of Riemannian optimization
  Nachuan Xiao, Xiaoyin Hu*, Xin Liu, Kim-Chuan Toh
  Mathematical Programming Computation, 2025, 17(2): 173-230. arXiv
  

• A Riemannian dimension-reduced second order method with application in sensor network localization
  Tianyun Tang, Kim-Chuan Toh, Nachuan Xiao*, Yinyu Ye
  SIAM Journal on Scientific Computing, 2024, 46(3): A2025-A2046.
  

• A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold
  Xin Liu, Nachuan Xiao*, Ya-xiang Yuan
  Journal of Scientific Computing, 2024, 99, Article 30.
  

• Adam-family methods for nonsmooth optimization with convergence guarantees
  Nachuan Xiao, Xiaoyin Hu*, Xin Liu, Kim-Chuan Toh
  Journal of Machine Learning Research, 2024, 25(48): 1-53.
  

• A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold
  Xiaoyin Hu, Nachuan Xiao*, Xin Liu, Kim-Chuan Toh
  IMA Journal of Numerical Analysis, 2024, 44(6): 3717-3748. arXiv
  

• Convergence properties of stochastic proximal subgradient method in solving a class of composite optimization problems with cardinality regularizer
  Xiaoyin Hu, Xin Liu, Nachuan Xiao*
  Journal of Industrial and Management Optimization, 2024, 20(5): 1934-1950.
  

• Dissolving constraints for Riemannian optimization
  Nachuan Xiao, Xin Liu, Kim-Chuan Toh*
  Mathematics of Operations Research, 2024, 49(1): 366-397.
  

• Solving optimization problems over the Stiefel manifold by smooth exact penalty functions
  Nachuan Xiao, Xin Liu*
  Journal of Computational Mathematics, 2024, 42(5): 1246-1276. arXiv
  

• An improved unconstrained approach for bilevel optimization
  Xiaoyin Hu, Nachuan Xiao*, Xin Liu, Kim-Chuan Toh
  SIAM Journal on Optimization, 2023, 33(4): 2801-2829.
  

• A class of smooth exact penalty function methods for optimization problems with orthogonality constraints
  Nachuan Xiao, Xin Liu*, Ya-xiang Yuan
  Optimization Methods and Software, 2022, 37(4): 1205-1241.
  

• Exact penalty function for ℓ_2,1 norm minimization over the Stiefel manifold
  Nachuan Xiao, Xin Liu*, Ya-xiang Yuan
  SIAM Journal on Optimization, 2021, 31(4): 3097-3126.