Papers

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Google Scholar

Preprints

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• Developing Lagrangian-based methods for nonsmooth nonconvex optimization
  Nachuan Xiao, Kuangyu Ding*, Xiaoyin Hu, Kim-Chuan Toh
  arXiv preprint arXiv:2404.09438.
  

• Decentralized stochastic subgradient methods for nonsmooth nonconvex optimization
  Siyuan Zhang, Nachuan Xiao, Xin Liu*
  arXiv preprint arXiv:2403.11565.
  

• Adam-family methods with decoupled weight decay in deep learning
  Kuangyu Ding, Nachuan Xiao*, Kim-Chuan Toh
  arXiv preprint arXiv:2310.08858.
  

• Convergence guarantees for stochastic subgradient methods in nonsmooth nonconvex optimization
  Nachuan Xiao, Xiaoyin Hu*, Kim-Chuan Toh
  arXiv preprint arXiv:2307.10053.
  

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

• CDOpt: a Python package for a class of Riemannian optimization
  Nachuan Xiao, Xiaoyin Hu*, Xin Liu, Kim-Chuan Toh
  arXiv preprint arXiv:2212.02698.
  

Publications

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$^{*}$: corresponding author

• 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 (to appear).
  
• 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 99(30), 2024.
  
• Adam-family methods for nonsmooth optimization with convergence guarantees
  Nachuan Xiao, Xiaoyin Hu*, Xin Liu, Kim-Chuan Toh
  Journal of Machine Learning Research 25(48):1-53, 2024.
  
• 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 (to appear).
  
• 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 (to appear).
  
• Dissolving constraints for Riemannian optimization
  Nachuan Xiao, Xin Liu, Kim-Chuan Toh*
  Mathematics of Operations Research (to appear).
  
• Solving optimization problems over the Stiefel manifold by smooth exact penalty function
  Nachuan Xiao, Xin Liu*
  Journal of Computational Mathematics (to appear).
  
• 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 $\ell_{2,1}$ norm minimization over the Stiefel manifold
  Nachuan Xiao, Xin Liu*, Ya-xiang Yuan
  SIAM Journal on Optimization, 2021, 31(4): 3097-3126.