Xin Liu
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Publications of Xin Liu

Published Papers and Preprints

  • L. Wang, N. Xiao and X. Liu, A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints (under review). link

  • Y. Hu, J. Yin, X. Gao, X. Liu and H. Song, Projected gradient descent algorithm for ab initio crystal structure relaxation under a fixed unit cell volume, Physical Review B, 109(2024), 224108. link

  • S. Zhang, N, Xiao and X. Liu, Decentralized Stochastic Subgradient Methods for Nonsmooth Nonconvex Optimization (under review). link

  • L. Wang, L. Bao and X. Liu, A Decentralized Proximal Gradient Tracking Algorithm for Composite Optimization on Riemannian Manifolds (under review). link

  • S. Liu, L. Wang, N. Xiao and X. Liu, An Inexact Preconditioned Zeroth-order Proximal Method for Composite Optimization (under review). link

  • X. Hu, X. Liu and 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 (2024), 1934-1950. link

  • T. Gu et al., BBGP-sDFO: Batch Bayesian and Gaussian Process Enhanced Subspace Derivative Free Optimization for High-Dimensional Analog Circuit Synthesis, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 43-2 (2023), 417-430. link

  • Y. Hu, M. Li, X. Liu and C. Meng, Sampling-Based Approaches for Multimarginal Optimal Transport Problems with Coulomb Cost, Mathematics of Computation (2024). link

  • X. Liu, Optimization Models and Approaches for Strongly Correlated Electrons Systems, Mathematica Numerica Sinica (in Chinese), 45-2 (2023), 141-159. link

  • N. Xiao, X. Hu, X. Liu and K. Toh, Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees, Journal of Machine Learning Research, 25-48 (2024), 1-53. link

  • N. Xiao, X. Liu and K. Toh, A Partial Exact Penalty Function Approach for Constrained Optimization (under review). link

  • L. Wang and X. Liu, Smoothing Gradient Tracking for Decentralized Optimization over the Stiefel Manifold with Non-smooth Regularizers, Proceedings of the 2023 62nd IEEE Conference on Decision and Control, (2024). link

  • N. Xiao, X. Hu, X. Liu and K. Toh, CDOpt: A Python Package for a Class of Riemannian Optimization (under review). link

  • L. Wang and X. Liu, A Variance-Reduced Stochastic Gradient Tracking Algorithm for Decentralized Optimization with Orthogonality Constraints, Journal of Industrial and Management Optimization, 19-10 (2023), 7753-7776. link

  • X. Hu, N. Xiao, X. Liu and K. Toh, An Improved Unconstrained Approach for Bilevel Optimization, SIAM Journal on Optimization, 33-4 (2023), 2801-2829. link

  • Y. Hu and X. Liu, The Exactness of the L1 Penalty Function for a Class of Mathematical Programs with Generalized Complementarity Constraints, Fundamental Research, DOI: 10.1016/j.fmre.2023.04.006. link

  • X. Hu, N. Xiao, X. Liu and K. Toh, A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold, IMA Journal of Numerical Analysis (2024). link

  • Y. Hu, X. Gao, Y. Zhao, X. Liu and H. Song, A Force-based Gradient Descent Method for Ab initio Atomic Structure Relaxation, Physical Review B, 106(2022), 104101. link

  • W. Liu, X. Liu and X. Chen, An Inexact Augmented Lagrangian Algorithm for Training Leaky ReLU Neural Network with Group Sparsity, Journal of Machine Learning Research, 24.212 (2023), 1-43. link

  • Y. Hu and X. Liu, The Convergence Properties of Infeasible Inexact Proximal Alternating Linearized Minimization, SCIENCE CHINA Mathematics, 66-10 (2023), 2385-2410. link

  • S. Zhou, X. Liu and L. Xu, Stochastic Gauss-Newton Algorithms for Online PCA, Journal of Scientific Computing, 96-3 (2023), 72. link

  • N. Xiao, X. Liu and K. Toh, Dissolving Constraints for Riemannian Optimization, Mathematics of Operations Research (2023). link

  • L. Wang and X. Liu, Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function, IEEE Transactions on Signal Processing, 70 (2022), 3029-3041. link

  • Y. Xu, X. Liu, X. Cao, et al., Artificial Intelligence: A Powerful Paradigm for Scientific Research, The Innovation, 2-4(2021), 100179. link

  • Y. Hu, H. Chen and X. Liu, A Global Optimization Approach for Multi-Marginal Optimal Transport Problems with Coulomb Cost, SIAM Journal on Scientific Computing, 45-3 (2023), A1214-A1238. link

  • N. Xiao and X. Liu, Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function, Journal of Computational Mathematics, 42-5 (2024), 1246-1276. link

  • W. Liu, X. Liu and X. Chen, Linearly-constrained Nonsmooth Optimization for Training Autoencoders, SIAM Journal on Optimization, 32-3 (2022), 1931-1957. link

  • X. Liu, N. Xiao and Y. Yuan, A Penalty-free Infeasible Approach for a Class of Nonsmooth Opimtization Problems over the Stiefel Manifold, Journal of Scientific Computing, 30 (2024), 99. link

  • L. Wang, X. Liu and Y. Zhang, A Communication-Efficient And Privacy-Aware Distributed Algorithm for Sparse PCA, Computational Optimization and Applications, 85 (2023), 1033–1072. link

  • L. Wang, X. Liu and Y. Zhang, Seeking Consensus on Subspaces in Federated Principal Component Analysis, Journal of Optimization Theory and Applications, DOI:10.1007/s10957-024-02523-1 (2024). link

  • L. Wang, B. Gao and X. Liu, Multipliers Correction Methods for Optimization Problems Over Stiefel Manifold, CSIAM Transactions on Applied Mathematics, 2 (2021), 508-531. link

  • X. Liu, Z. Wen and Y. Yuan, Subspace Methods for Nonlinear Optimization, CSIAM Transactions on Applied Mathematics, 2 (2021), 585-651. link

  • B. Gao, G. Hu, Y. Kuang and X. Liu, An Orthogonalization-free Parallelizable Framework for All-electron Calculations in Density Funcitonal Theory, SIAM Journal on Scientific Computing, 44-3 (2022), B723-B745. link

  • N. Xiao, X. Liu and Y. Yuan, Exact Penalty Function for L21 Norm Minimization over the Stiefel Manifold, SIAM Journal on Optimization, 31-4 (2021), 3097-3126. link

  • N. Xiao, X. Liu and Y. Yuan, A Class of Smooth Exact Penalty Function Methods for Optimization Problems with Orthogonality Constraints, Optimization Methods and Software, DOI:10.1080/10556788.2020.1852236, 2020. link

  • Q. Dong, X. Yao, X. Liu, B. Liu and G. Zhai, Pseudo Complementary Measurement for the Traditional Single-pixel Camera, Chinese Physics B, 29-11 (2020), 114202. link

  • J. Hu, X. Liu, Z. Wen and Y. Yuan, A Brief Introduction to Manifold Optimization, Journal of the Operations Research Society of China, 8 (2020), 199-248. link

  • L. Wu, X. Liu and Z. Wen, Best Symmetric Rank-1 Approximation of Symmetric High-order Tensors, Optimization Methods and Software, 35-2 (2020), 416-438. link

  • Y. Shen and X. Liu, An Alternating Minimization Method for Matrix Completion Problems, Discrete and Continuous Dynamical Systems, 13-6 (2020), 1757-1772. link

  • B. Gao, X. Liu and Y. Yuan, Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints, SIAM Journal on Scientific Computing, 41-3(2019), A1949–A1983. link

  • Y. Shen, H. Xu and X. Liu, An Alternating Minimization Method for Robust Principal Component Analysis, Optimization Methods and Software, 34-6 (2019), 1251-1276. link

  • C. Ma, X. Liu and Z. Wen, Globally Convergent Levenberg-Marquardt Method for Phase Retrieval, IEEE Transactions on Information Theory, 65-4 (2019), 1557-9654. link

  • Y. Liu, X. Liu and S. Ma, On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming, Mathematics of Operations Research, 44-2(2019), 632-650. link

  • C. Chen, M. Li, X. Liu and Y. Ye, Extended ADMM and BCD for Nonseparable Convex Minimization Models with Quadratic Coupling Terms: Convergence Analysis and Insights, Mathematical Programming, 173(2019), 37-77. link

  • X. Liu, M. Ng, R. Zhang and Z. Zhang, A Continuous Optimization Model for Clustering, Mathematic Numerica Sinica (in Chinese), 40-4 (2018), 354-366. link

  • B. Gao, X. Liu, X. Chen and Y. Yuan, A New First-order Algorithmic Framework for Optimization Problems with Orthogonality Constraints, SIAM Journal on Optimization, 28-1(2018), 302–332. link

  • H. Wang, X. Liu, X. Chen and Y. Yuan, SNIG Property of Matrix Low-rank Factorization Model, Journal of Computational Mathematics, 36-3 (2018), 374-390. link

  • B. Gao, X. Liu and Y. Yuan, Algorithms for Optimization Problems with Orthogonality Constraints, OR Transactions (in Chinese), 21-4 (2017), 57-68. link

  • J. Hu, B. Jiang, X. Liu and Z. Wen, A Note on Semidefinite Programming Relaxations for Polynomial Optimization Over a Single Sphere, SCIENCE CHINA Mathematics, 59-8 (2016), 1543-1560. link

  • Z. Wen, C. Yang, X. Liu and Y. Zhang, Trace-Penalty Minimization for Large-scale Eigenspace Computation, Journal of Scientific Computing, 66-3 (2016), 1175-1203. link

  • X. Liu, Z. Wen and Y. Zhang, An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations, SIAM Journal on Optimization, 25-3 (2015), 1571–1608. link

  • X. Liu, Z. Wen, X. Wang, M. Ulbrich and Y. Yuan, On the Analysis of the Discretized Kohn-Sham Density Functional Theory, SIAM Journal on Numerical Analysis, 53-4 (2015), 1758–1785. link

  • Q. Dong, X. Liu, Z. Wen and Y. Yuan, A Parallel Line Search Subspace Correction Method for Convex Optimization Problems, Journal of the Operations Research Society of China, 3 (2015), 163-187. link

  • X. Liu, X. Wang, Z. Wen and Y. Yuan, On the Convergence of the Self-Consistent Field Iteration in Kohn-Sham Density Functional Theory, SIAM Journal on Matrix Analysis and Applications, 35-2 (2014), 546-558. link

  • X. Liu, Z. Wen and Y. Zhang, Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions, SIAM Journal on Scientific Computing, 35-3 (2013), A1641-A1668. link

  • X. Liu, C. Hao and M. Cheng, A Sequential Subspace Project Method for Linear Eigenvalue Problem, Asia Pacific Journal of Operational Research, 30-3 (2013). link

  • Z. Wen, C. Yang, X. Liu and S. Machesini, Alternating Direction Methods for Classical and Ptychographic Phase Retrieval, Inverse Problems, 28-11 (2012). link

  • Z. Wen, W. Yin, X. Liu and Y. Zhang, Introduction to Compressive Sensing and Sparse Optimization (in Chinese), OR Transactions, 16-3 (2012), 49-64. link

  • X. Liu, S. McKeeb, J. Yuan and Y. Yuan, Uniform Bounds on the 1-norm of the Inverse of Lower Triangular Toeplitz Matrices, Linear Algebra and its Applications, 435 (2011), 1157–1170. link

  • X. Liu, Numerical Methods for Special Nonlinear Least Squares Problems and L1 Norm Minimization Problems (in Chinese), Ph.D. thesis, AMSS, CAS (2009). pdf

  • X. Liu, Global Minimization of Quadratic Least-Squares Problems, Global-Link Informatics Limited, Hong Kong, Proceedings of the Ninth National Conference of Operation Research Society of China (2008), 188-193.

  • X. Liu and Y. Yuan, On the Separable Nonlinear Least Squares Problems, Journal of Computational Mathematics, 26 (2008), 390-403. link

  • X. Liu, An Efficient Unseparated Scheme for Separable Nonlinear Least Squares Problem, Global-Link Informatics Limited, Hong Kong, Proceedings of the Eighth National Conference of Operation Research Society of China (2006), 132-137.

  • X. Liu, Optimization Methods for Large-scale Sylvester Equation and the Separation of two Matrices, B.Sc. thesis, SMS, PKU (2004). pdf