Xin Liu (刘歆)
Professor, Doctoral Supervisor

State Key Laboratory of Scientific and Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing
Academy of Mathematics and System Sciences (AMSS)
Chinese Academy of Sciences (CAS)
Contact Information

Address: 55, Zhong Guan Cun East Road, Beijing 100190, China
Office: LBB-302, AMSS, CAS

Email: liuxin at lsec.cc.ac.cn
Research Interests

My recent research mainly focuses on numerical methods for optimization problems with orthogonality constraints including linear and nonlinear eigenvalue problems. The theoretical and computational studies on nonlinear least squares probems related to phase retrieval, matrix factorization and deep learning always attract my attention. I am also interested in distributed optimiztion approaches which cater to the increasing demands of high performance computing arisen from various science and engineering areas.

Education

Ph.D. in Computational Mathematics (2009.6)
University of Chinese Academy of Sciences
(Academy of Mathematics and System Sciences, Chinese Academy of Sciences)
Advisor: Professor Ya-xiang Yuan

B.S. in Computational Mathematics (2004.6)
School of Mathematics Sciences, Peking University
Working Experience

Academy of Mathematics and System Sciences (AMSS), Chinese Academy of Sciences (CAS)

    Professor (2020.4 - present)

    Doctoral supervisor (2018.6 - present)

    Associate professor (2015.3 - present)

    Assistant professor (2009.7 - 2015.3)

Courant Institute, New York University

    Visiting scholar (2016.10 - 2017.3)

    Host: Michael L. Overton

CAAM, Rice University

    Visiting scholar (2010.9 - 2011.8)

    Hosts: Yin Zhang, Wotao Yin

Konrad-Zuse-Zentrum für Informationstechnik Berlin(ZIB)

    Postdoc (2009.9 - 2010.8)

    Hosts: Martin Grötschel, Thorsten Koch

Social Activities

The Chinese Association of Young Scientists And Technologists

    Council member (2019.12 - present)

China Society for Industrial and Applied Mathematics (CSIAM)

    Deputy secretary-general (2019.5 - present)

CAS AMSS-PolyU Joint Laboratory of Applied Mathematics

    Associate director (2018.11 - present)

Youth Innovation Promotion Association of Chinese Academy of Sciences

    Member (2017.1 - present)

    Vice president of the Branch of Mathematical and Physical Sciences (2018.5 - present)

The Chinese Mathematical Society (CMS)

    Council member of the Beijing branch of the computational mathematics branch (2017.9 - present)

Acta Physica Sinica

    Guest editor (2018.6 - present)

Mathematica Numerica Sinica

    Associate editor (2017.7 - present)

Mathematical Programming Computation

    Associate editor (2015.7 - present)

The Operations Research Society of China (ORSC)

    Council member (2016.10 - present)

    Young council member of the mathematical programming branch (2014.5 - 2019.4)

    General secretary of the scientific popularization committee (2013.1 - 2016.12)

    Council member of the Beijing branch (2011.12 - 2019.11)

    Executive council member of the Beijing branch (2019.12 - present)

Selected Awards

    Morning Star Award from Beijing Branch of CAS (2017)

    Science and Technology Award for Youth from ORSC (2016)

    Excellent Youth Grant of the National Natural Science Foundation of China (2016)

    Jingrun Chen Future Star Program of AMSS (2014)

基本信息

刘歆 研究员, 博士生导师

中国科学院 数学与系统科学研究院
计算数学与科学工程计算研究所
科学与工程计算国家重点实验室
联系方式

北京市海淀区中关村东路55号科技综合楼(蓝白楼)302
邮政编码: 100190
办公室电话: +86-10-8254-1041
电子邮件地址: liuxin at lsec.cc.ac.cn
教育经历

理学博士, 专业: 计算数学 (2009.6)
中国科学院研究生院(现: 中国科学院大学)
(培养单位: 中国科学院数学与系统科学研究院)
导师: 袁亚湘 院士

理学学士, 专业: 计算数学 (2004.6)
北京大学数学科学学院
工作经历

中国科学院数学与系统科学研究院

    研究员 (2020.4 - 现在)

    博士生导师 (2018.6 - 现在)

    副研究员 (2015.3 - 现在)

    助理研究员 (2009.7 - 2015.3)

纽约大学, 柯朗研究所

    访问学者 (2016.10 - 2017.3)

    合作者: Michael L. Overton

莱斯大学, 计算与应用数学系

    访问学者 (2010.9 - 2011.8)

    合作者: 张寅, 印卧涛

德国ZIB研究所(Konrad-Zuse-Zentrum für Informationstechnik Berlin)

    博士后 (2009.9 - 2010.8)

    合作者: Martin Grötschel, Thorsten Koch

社会兼职

中国青年科技工作者协会

    理事 (2019.12 - 现在)

中国工业与应用数学学会 (CSIAM)

    副秘书长 (2019.5 - 现在)

共青团中国科学院委员会

    第十六届委员 (2018.12 - 现在)

中国科学院数学与系统科学研究院-香港理工大学“应用数学”联合实验室

    副主任 (2018.11 - 现在)

中国科学院青年创新促进会

    会员 (2017.1 - 现在)

    数理分会副会长 (2018.5 - 现在)

中国数学会 (CMS)

    北京市计算数学会理事 (2017.9 - 现在)

物理学报

    特约栏目编辑 (2018.6 - 现在)

计算数学

    编委 (2017.7 - 现在)

Mathematical Programming Computation

    编委 (2015.7 - 现在)

中国运筹学会 (ORSC)

    理事 (2016.10 - 现在)

    数学规划分会青年理事 (2014.5 - 现在)

    科普工作委员会秘书长 (2013.1 - 2016.12)

    北京市运筹学会理事 (2011.12 - 2019.11)

    北京市运筹学会常务理事 (2019.12 - 现在)

部分获奖经历

    中国科学院北京分院‘‘启明星”优秀人才(2017)

    中国运筹学会青年科技奖(2016)

    国家自然科学基金委国家优秀青年科学基金(2016)

    中国科学院数学与系统科学研究院‘‘陈景润未来之星”计划(2014)


Selected Grants
As the Principal Investigator

    2019.09-2024.09, 中国科学院基础前沿科学计划从0到1原始创新项目-ZDBS-LY-7022, 人工智能中优化问题的方法和理论, 100万, 课题负责人

    2020.01-2023.12, 国家自然科学基金面上项目-11971466, 分布式优化的理论与算法, 52万， 课题负责人

    2018.01-2018.12, 国家自然科学基金专项基金-11726617, 正交非负矩阵分解的算法、理论与应用, 20万, 课题负责人

    2017.01-2019.12, 国家优秀青年科学基金项目-11622112, 最优化理论与方法, 150万, 课题负责人

    2015.01-2018.12, 国家自然科学基金面上项目-11471325, 矩阵分解问题的优化算法与理论, 60万, 课题负责人

    2012.01-2014.12, 国家自然科学基金青年项目-11101409, 几类矩阵优化问题的算法设计及其理论和应用, 22万元, 课题负责人

As a Member

    2017.01-2019.12, 中国科学院前沿科学重点项目-QYZDJ-SSW-SYS010, 第一原理电子结构计算的方法与理论, 课题组成员

    2016.01-2018.12, 国家自然科学基金重大研究计划-91530204, 集合变分同化的子空间方法研究, 课题组成员

    2015.01-2018.12, 国家自然科学基金国际(地区)合作与交流项目-11461161005, 稀疏优化算法与理论, 课题组成员

    2014.01-2018.12, 国家自然科学基金重点项目-11331012, 面向信息技术的优化理论和方法, 课题组成员

    2013.12-2016.12, 国家863计划项目-2013AA122902, 被动光学高光谱强度关联成像技术, 课题组成员


Collaborators and Students
Long Term Collaborators

    Ya-xiang Yuan, Academy of Mathematics and System Sciences, Chinese Academy of Sciences

    Zaiwen Wen, Peking University

    Yin Zhang, Rice University

    Xiaojun Chen, The Hong Kong Polytechnic University

    Chao Yang, Lawrence Berkeley National Laboratory

Cooperant Students

    Qian Dong (2012.9-2016.6), AMSS (now works for Institute of Software, CAS)

    Hong Wang (2013.12-2015.12), PolyU (now works for Huawei)

    Bin Gao (2015.3-2019.8), AMSS (now works for UCLouvain)

    Nachuan Xiao (2017.3-), AMSS

    Bastien Vieublé (2019.5-2019.9), ENSEEIHT, France

    Siyun Zhou (2019.9-), UESTC

Graduate Students

    Yadan Chen (2016.9-), from Jilin University

    Wei Liu (2017.9-), from Zhejiang University

    Lei Wang (2018.9-), from University of Chinese Academy of Sciences

    Yukuan Hu (2019.9-), from Tongji University

    Shanglin Liu (2020.9-), from Xi'an Jiaotong University

Guaduates

    Rui Zhang (2015.9-2017.7), from Taiyuan University of Technology, Master Degree (now works for Inspur),
    co-supervised by Zaikun Zhang

Undergraduate Students

    Zhimin Peng (2010.7-2010.8), UCLA (now works for Twilio Inc.)

    Xinyang Wang (2013.9-2014.6), Courant, NYU (now works for Facebook)

    Chao Ma (2015.9-2016.6), Princeton (now works for Stanford)

    Donghao Ying (2019.9-), UCAS



Publications of Xin Liu
Published Papers and Preprints

    N. Xiao, X. Liu and Y. Yuan, A Class of Smooth Exact Penalty Function Methods for Optimization Problems with Orthogonality Constraints, Mathematical Programming (under review). link

    J. Hu, X. Liu, Z. Wen and Y. Yuan, A Brief Introduction to Manifold Optimization, Journal of the Operations Research Society of China (DOI: 10.1007/s40305-020-00295-9). 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 Framework for Orthogonal Constrained Optimization Problems, 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

Working Papers

    B. Gao, X. Liu, X. Chen and Y. Yuan, On the Łojasiewicz Exponent of Quadratic Sphere Constrained Optimization Problem.

    Z. Wen. X. Peng, X. Liu, X. Bai and X. Sun, Asset Allocation under the Basel Accord Risk Measures.


Solvers
Dominant Eigenpair Computation

LMSVD is an adaptive Krylov subspace algorithm for dominant singular value decomposition.

Code: MATLAB File Exchange
(In the case you like this code, please rate it, thanks.)

Reference:
Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions (SIAM Journal on Scientific Computing).
400px     

SLRP is a Gauss Newton method of symmetric low-rank product for calculating dominant eigenspace.

Code: two lines in MATLAB (Please see to the left.)

Reference:
An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations (SIAM Journal on Optimization).

Optimization Problems with Orthognality Constraints
400px     

FOForth is a first-order framework for solving optimization problems with orthognality constraints, including three algorithms: gradient reflection, gradient projection and column-wise block coordinate descend.

Code: MATLAB File Exchange

Reference:
A First-Order Framework for optimization problems with orthogonality constraints (SIAM Journal on Optimization).

450px     

PCAL is a parallelizable approach for solving optimization problems with orthognality constraints.

Code: MATLAB File Exchange

Reference:
Parallelizable Column-wise Augmented Lagrangian approaches for optimization with orthogonality constraints (SIAM Journal on Scientific Computing).



Conferences Participated or Organized
Selected Presentations

    2019.08, The Sixth International Conference on Continuous Optimization, Berlin, Germany

    2019.07, The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Valencia, Spain

    2018.07, The 29th European Conference on Operational Research, Valencia, Spain

    2018.07, The 23nd International Symposium on Mathematical Programming (ISMP 2018), Bordeaux, France

    2018.05, SIAM Conference on SIAM Conference on Applied Linear Algebra (SIAMALA 2018), Hong Kong, China

    2017.07, SIAM Annual Meeting (SIAMAN 2017), Pittsburgh, United States

    2017.05, SIAM Conference on Optimization (SIAMOP 2017), Vancouver, Canada

    2016.09, Continuous Optimization: Challenges and Applications, Haifa, Israel

    2016.08, The Fifth International Conference on Continuous Optimization, Tokyo, Japan

    2016.07, Mathematical and Numerical Analysis of Electronic Structure Models, Roscoff, France

    2015.08, The 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), Beijing, China

    2015.07, The 22nd International Symposium on Mathematical Programming (ISMP 2015), Pittsburgh, United States

    2015.03, 6th International Conference on High Performance Scientific Computing, Hanoi, Vietnam

    2014.10, The 3rd Workshop on Optimization and Risk Management, Hong Kong, China

    2014.05, Southern California Optimization Day, San Diego, United States

    2014.05, SIAM Conference on Optimization (SIAMOP 2014), San Diego, United States

    2013.12, International Conference on Engineering and computational Mathematics, Hong Kong, China

    2013.09, Sino-German Symposium on Operations Research, Spitzingsee, Germany

    2013.09, The 9th International Conference on Numerical Optimization and Numerical Linear Algebra, Changchun, Jilin, China

    2013.07, The Fourth International Conference on Continuous Optimization, Lisbon, Portugal

    2013.06, The 11th EUROPT Workshop on Advances in Continuous Opitmization, Firenze, Italy

    2012.10, Fifteenth Chinese-American Kavli Frontiers of Science Symposium, Irvine, California, United States

    2012.09, The 2nd Sino-German Workshop on Optimization, Modeling, Methods and Applications in Industry and Management, Beijing, China

    2012.08, The 21st International Symposium on Mathematical Programming (ISMP 2012), Berlin, Germany

    2012.05, The 3rd Conference on Optimization Methods and Software, Chania, Crete, Greece

    2011.11, The 8th International Conference on Numerical Optimization and Numerical Linear Algebra, Xiamen, Fujian, China

    2011.09, The 5th Sino-Japan Optimization Meeting, Beijing, China

    2011.08, Sino-German Workshop on Optimization, Modeling, Methods and Applications in Industry and Management, Berlin, Germany

    2011.07, The 7th International Congress on Industrial and Applied Mathematics (ICIAM 2011), Vancouver, Canada

    2011.05, SIAM Conference on Optimization (SIAMOP 2011), Darmstadt, Germany

    2010.08, Sino-German Workshop on Algorithm Engineering, Shanghai, China

    2009.08, The 20th International Symposium of Mathematical Programming (ISMP 2009), Chicago, Illinois, United States

    2009.08, The 7th International Conference on Numerical Optimization and Numerical Linear Algebra, Lijiang, Yunnan, China

    2008.07, The VII Brazilian Workshop on Continuous Optimization, Campinas, Sao Paulo, Brazil

    2007.09, The 6th International Conference on Numerical Linear Algebra and Optimization, Urumqi, Xinjiang, China

    2007.07, The 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), Zurich, Switzerland

    2006.09, International Conference on Numerical Analysis and Optimization dedicated to M.J.D. Powell’s 70th Birthday, Beijing, China

Conferences Organized

    2020.5, SCF - Youth Online Forum

    2019.12, The First Workshop on Mathematical Theory in Artificial Intelligence

    2019.12, The 5th Youth Symposium on Scientific and Engineering Computing of Scientific Computing Forum

    2019.4, The 12th ICNONLA

    2019.4, International Conference on Mathematical Optimization

    2018.9, The 4th Youth Symposium on Scientific and Engineering Computing of Scientific Computing Forum

    2018.8, Short Course: Recent progress in non-convex optimization for machine learning

    2017.9, The 3rd Youth Symposium on Scientific and Engineering Computing of Scientific Computing Forum

    2017.8, Short Course: Methods of Structural Optimization for Large-Scale Optimization Problems

    2017.8, The 11th ICNONLA

    2017.6, Forum on Applied Mathematics in Data Science: schedule

    2017.5, Invited Workshop: Big Data Analysis with Applications in ECM 2017

    2016.9, The 2nd Youth Symposium on Scientific and Engineering Computing

    2016.8, The 2nd Graduated Stundent Forum of the Mathematical Programming Branch of ORSC

    2016.8, ICNAAO (dedicated to late professor M.J.D. Powell)

    2015.12, Youth Symposium on Scientific and Engineering Computing

    2015.8, The 10th ICNONLA

    2013.9, The 9th ICNONLA

    2011.11, The 8th ICNONLA


Courses for Undergraduate Students
Univerisity of Chinese Academy of Sciences

    Calculus Exercise I (2014.9-2015.1)

    Calculus Exercise II (2015.3-2015.7)

    Calculus Exercise III (2015.9-2016.1)

    Analytical Geometry (2015.11)


Courses for Undergraduate StudentsUsersliuxin_Websitegrad.jemdoc
Univerisity of Chinese Academy of Sciences

    Convex Analysis (2020.2-2020.4)

    Selected Topics on the Optimization Approaches for Big Data Analysis (2019.6)

    Convex Analysis (2019.2-2019.4)

    Selected Topics on the Optimization Approaches for Big Data Analysis (2018.7)

    Convex Analysis (2018.3-2018.5)

    Selected Topics on the Optimization Approaches for Big Data Analysis (2017.7)

    Convex Analysis (2017.4-2017.5)

    Selected Topics on the Optimization Approaches for Big Data Analysis (2016.7)

    Selected Topics on the Optimization Approaches for Big Data Analysis (2015.6)

Useful Materials

    Talk in Prof. Jinchao Xu's Deep Learning Seminar (2017.3)