XIAO, Nachuan

Assistant Professor

Education Background

Ph.D. in Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

B.S. in Mathematics, Fudan University

Research Field
Constrained Optimization, Nonsmooth Optimization, Stochastic Optimization
Personal Website
https://xnchxy.github.io/
Office
Room 614, Teaching Complex B
Biography

Dr. Nachuan Xiao is an Assistant Professor at the School of Data Science, Chinese University of Hong Kong (Shenzhen). He received his Ph.D. from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2021 under the supervision of Prof. Ya-xiang Yuan. After that, he joined the Institute of Operations Research and Analytics at the National University of Singapore as Research Fellow, working with Prof. Kim-Chuan Toh. His research focuses computational optimization, especially on developing efficient numerical methods for nonconvex constrained optimization problems. His work has been published in top Journals in the fields of optimization and machine learning, including SIAM Journal on Optimization, Mathematics of Operations Research, Journal of Machine Learning Research, Mathematical Programming Computation, and IMA Journal of Numerical Analysis.

Academic Publications

  1. X. Hu, N. Xiao*, X. Liu, K.-C. Toh, "Learning-rate-free momentum SGD with reshuffling converges in nonsmooth nonconvex optimization", Journal of Scientific Computing 102(85), 2025

  2. N. Xiao, X. Hu*, X. Liu, K.-C. Toh, "CDOpt: a Python package for a class of Riemannian optimization", Mathematical Programming Computation 1-58, 2025

  3. T. Tang, K.-C. Toh, N. Xiao*, Y. Ye, "A Riemannian dimension-reduced second order method with application in sensor network localization", SIAM Journal on Scientific Computing 46(3) A2025-A2046, 2024

  4. X. Liu, N. Xiao*, Y.-x. Yuan, "A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold", Journal of Scientific Computing 99(30), 2024

  5. N. Xiao, X. Hu*, X. Liu, K.-C. Toh, "Adam-family methods for nonsmooth optimization with convergence guarantees", Journal of Machine Learning Research 25(48) 1-53, 2024

  6. X. Hu, N. Xiao*, X. Liu, K.-C. Toh, "A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold", IMA Journal of Numerical Analysis, drad098, 2023

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

  8. N. Xiao, X. Liu, K.-C. Toh*, "Dissolving constraints for Riemannian optimization", Mathematics of Operations Research 49(1) 366-397, 2024

  9. N. Xiao, X. Liu*, "Solving optimization problems over the Stiefel manifold by smooth exact penalty function", Journal of Computational Mathematics (to appear), 2024+

  10. X. Hu, N. Xiao*, X. Liu, K.-C. Toh, "An improved unconstrained approach for bilevel optimization", SIAM Journal on Optimization 33(4) 2801-2829, 2023

  11. N. Xiao, X. Liu*, Y.-x. Yuan, "A class of smooth exact penalty function methods for optimization problems with orthogonality constraints", Optimization Methods and Software 37(4) 1205-1241, 2022

  12. N. Xiao, X. Liu*, Y.-x. Yuan, "Exact penalty function for L21​-norm minimization over the Stiefel manifold", SIAM Journal on Optimization 31(4) 3097-3126, 2021