Welcome to Defeng Sun's Home Page

Defeng SUN (孫德鋒) Chair Professor Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong

Education Research Interests Teaching Recruitments Professional Activities Recognitions Codes Some Recent Talks Some Old Talks Publications

SUN Defeng

Department of Applied Mathematics
The Hong Kong Polytechnic University 
Hung Hom, Kowloon, Hong Kong

Office: TU 728, Yip Kit Chuen Building

Phone: +852 2766 6935

Fax: +852 2362 9045

Email: defeng.sun@polyu.edu.hk

Web: https://www.polyu.edu.hk/ama/profile/dfsun

Education

BSc (1989), MSc (1992) both from Nanjing University, Nanjing

PhD (1995) from Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing

Recent Research Interests

• Sparse Newton Methods with Low Complexities
• Matrix Optimization (MatOpt): Theory, Algorithms, Software and Applications
• High-Dimensional Statistical Optimization
• Second Order Variational Analysis
• Risk Management and Computational Finance

Teaching

• AMA615 Nonlinear Optimization Methods, Semester 1, 2020/2021; Wednesday (11:30-12:30) and Friday (11:30—13:30).

Recruitments

• PhD Students: I am particularly interested in students who have solid mathematical foundation and are willing to work hard on challenging problems in optimization and beyond. Drop me an email to request for more details. English requirement for PhD students (with or without a master degree): at least IELTS 6.5 or TOEFL 80. Also check the prestigious Hong Kong PhD Fellowship Scheme.
• Research Assistants/Research Fellows/Postdoctoral Fellows: multiple positions are available immediately; working on various optimization projects; computational skills are required.

Professional Activities

• President, The Hong Kong Mathematical Society (May 2020--)
• Organizing Committee Co-Chair and Local Organizing Committee Co-Chair, “SIAM Conference on Optimization (OP20)”, The Hong Kong Polytechnic University, Hong Kong, May 26-29, 2020. Rescheduled to 2021 and Relocated: https://www.siam.org/conferences/cm/conference/op21
• Program Committee Member, “The Sixth International Conference on Continuous Optimization (ICCOPT 2019)”, Berlin, August 5-8, 2019
• Program Committee Member, “The Fifth International Conference on Continuous Optimization (ICCOPT 2016)”, Tokyo, August 6-11, 2016.
• Associate Editor, Mathematical Programming (Series A, August 2007 --; Series B, January 2014--December 2017).
• Associate Editor, SIAM Journal on Optimization (January 2012--).
• Associate Editor, Journal of the Operations Research Society of China (2012--).
• Associate Editor, Journal of Computational Mathematics (2017--).
• Associate Editor, Science China Mathematics (January 2018 --).
• Advisory Committee Member, Asia-Pacific Journal of Operational Research (January 2014--); editor-in-chief (October 2010 –December 2013).
• Society Membership: INFORMS, SIAM, MOS, AMS, and etc.

Recognitions

• Elected a SIAM Fellow in 2020.
• Plenary speaker at “SIAM Conference on Computational Science and Engineering (CSE21)”, to be held at Fort Worth, Texas, USA, from March 1-5, 2021.
• Awarded the triennial Beale--Orchard-Hays Prize for Excellence in Computational Mathematical Programming 2018 by the Mathematical Optimization Society.
• Plenary speaker at “SIAM Conference on Optimization (OP11)”, Darmstadtium Conference Center, Darmstadt, Germany, May 16-19, 2011.
• The inaugural Outstanding Scientist Award, by Faculty of Science, National University of Singapore, 2007.
• Yilida Prize of the Chinese Academy of Sciences, 1995.
• Excellent Prize of the President of the Graduate School at the Chinese Academy of Sciences, 1994.

Codes in Matlab and others

Codes for nearest (covariance) correlation matrix problems

• Codes for the Nearest Correlation Matrix problem (the problem was initially introduced by Prof. Nick Higham): CorrelationMatrix.m is a Matlab code written for computing the nearest correlation matrix problem (first uploaded in August 2006; last updated on August 30, 2019). This code should be good enough for most Matlab users. If your Matlab version is very low and you really need a faster code, you can download mexeig.mexw64 (for win64 operating system) and if use win32 or Linux system, you need to download the installmex file installmex.m and the c-file mexeig.c by running the installmex.m first. For a randomly generated 3,000 by 3,000 pseudo correlation matrix (the code is insensitive to input data), the code needs 24 seconds to reach a solution with the relative duality gap less than 1.0e-3 after 3 iterations and 43 seconds with the relative duality gap less than 1.0e-10 after 6 iterations in my Dell Desktop with Intel (R) Core i7 processor and for an invalid 10,000 by 10,000 pseudo correlation matrix, the code needs 15 minutes to reach a solution with the relative duality gap less than 1.0e-4 after 4 iterations and 24 minutes with the relative duality gap less than 1.0e-12 after 7 iterations. For practitioners, you may set the stopping criterion (relative duality gap) to stay between 1.0e-1 and 1.0e-3 to run the code (typically, 1 to 3 iterations). If you need a C/C++ code, download main.c and main.h, which were written by Pawel Zaczkowski under a summer research project. If you are a client to The Numerical Algorithms Group (NAG), you may also enjoy their commercialized implementations. The code in R CorrelationMatrix.R was written by Ying Cui (yingcui@umn.edu) (last updated on August 31, 2019; for efficiency, please use Microsoft R open) and the code in Python CorrelationMatrix.py was written by Yancheng Yuan (e0009066@u.nus.edu) (last updated on May 11, 2017), respectively.
• CorNewton3.m Computing the Nearest Correlation Matrix with fixed diagonal and off diagonal elements (uploaded on September 14, 2009). The code in R CorNewton3.R was provided by Professor Luca Passalacqua (luca.passalacqua@uniroma1.it) (uploaded on October 7, 2016; for efficiency, please use Microsoft R open).
• CorNewton3_Wnorm.m Computing the W-norm Nearest Correlation Matrix with fixed diagonal and off diagonal elements Testing example: testCorMatWnorm.m (uploaded on September 14, 2009).
• CorMatHdm.m Calibrating the H-weighted Nearest Correlation Matrix Testing example: testCorMatHdm.m (uploaded in June 2008; last updated on September 10, 2009)
• CorMatHdm_general.m Computing the H-weighted Nearest Correlation Matrix with fixed elements and lower and upper bounds [H should not have too many zero elements for better numerical performance; otherwise, see CaliMatHdm] Testing example: testCorMatHdm_general.m (uploaded on September 14, 2009).
• LagDualNewton.m (this is superseded by CorNewton3.m) Testing example: testLagDualNewton.m (LagDualNewton method for the Band Correlation Stress Testing, "CorNewton1.m" will be called).
• CorNewtonSchur.m Testing example: testCorNewtonSchur.m (Schur decomposition based method for the Local Correlation Stress Testing, "CorNewton1.m" will be called).
• AugLagNewton.m (this is superseded by CorMatHdm_general.m) Testing example: testAugLagNewton.m (AugLagNewton method for the Band Correlation Stress Testing, "CorNewton1.m" will be called). (uploaded in March 2007).
• CaliMat1Mex.zip (Codes and testing example for) Calibrating Covariance Matrix Problems with Inequality and/or Equality Constraints (uploaded in April 2010)
• CaliMatHdm.zip Calibrating the H-weighted Nearest Covariance Matrix [H is allowed to have a large number of zero elements] (uploaded in April 2010).
• Rank_CaliMat.zip Calibrating the Nearest Correlation Matrix with Rank Constraints (uploaded in April 2010).
• Rank_CaliMatHdm.zip Calibrating the H-weighted Nearest Correlation Matrix with Rank Constraints (uploaded in April 2010; last updated in October 2010 by including the refined Major codes).

Codes under the Matrix Optimization (MatOpt) Project

• QSDPNAL (version 0.1): a MATLAB software for solving convex quadratic semidefinite programming (QSDP) (click here for an introduction on how to use the package) [CAUTION: this software is for research purpose. It is not intended nor designed to be a general purpose software at the moment.] For the details of the software, please check the following paper:

[Xudong Li, Defeng Sun, and Kim Chuan Toh, “QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming”, Mathematical Programming Computation, 10 (2018) 703--743.]

• SDPNAL+: a MATLAB software for solving large scale semidefinite programming with bound constraints (click here for an introduction on how to use the package) [awarded the triennial Beale–Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society at Bordeaux, France, July 2-6, 2018. See Picture 1, Picture 2, and Picture 3.] [CAUTION: this software is NOT designed for solving small to medium sized SDP problems, for which interior point methods based software such as SDPT3 is a better option.] For the details of the software, please check the following papers:

[Defeng Sun, Kim Chuan Toh, Yancheng Yuan, Xin-Yuan Zhao, SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0), to appear in Optimization Methods and Software (2019).]

[Liuqin Yang, Defeng Sun, and Kim Chuan Toh, SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints, Mathematical Programming Computation, 7 (2015), pp. 331-366.]

[Defeng Sun, Kim Chuan Toh, and Liuqin Yang, “A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type constraints”, SIAM Journal on Optimization Vol. 25, No. 2 (2015) 882–915. Detailed computational results for over 400 problems tested in the paper. You may also find a supplementary note here on more detailed comparisons between the performance of our proposed algorithm and various variants of ADMMs.]

[X.Y. Zhao, D.F. Sun, and Kim Chuan Toh, A Newton-CG augmented Lagrangian method for semidefinite programming, SIAM Journal on Optimization, 20 (2010), pp. 1737--1765.]

• "Solving log-determinant optimization problems by a Newton-CG proximal point algorithm". See the brief user's guide logdet-0-guide.pdf
• CorMatHdm_general.m Computing the H-weighted Nearest Correlation Matrix with fixed elements and lower and upper bounds [H should not have too many zero elements for better numerical performance; otherwise, see CaliMatHdm] Testing example: testCorMatHdm_general.m (uploaded on September 14, 2009).
• CaliMatHdm.zip Calibrating the H-weighted Nearest Covariance Matrix [H is allowed to have a large number of zero elements] (uploaded in April 2010).

Codes under the Statistical Optimization (StaOpt) Project

• SuiteLasso: a MATLAB suite for regression problems with generalized Lasso regularizers [last updated in January 2019]. See the introduction on how to use it.

Codes for rank constrained problems

• Rank_CaliMat.zip Calibrating the Nearest Correlation Matrix with Rank Constraints (uploaded in April 2010).
• Rank_CaliMatHdm.zip Calibrating the H-weighted Nearest Correlation Matrix with Rank Constraints (uploaded in April 2010; last updated in October 2010 by including the refined Major codes).

Codes for other problems

• IQEP_Newton.m Computing the Inverse Quadratic Eigenvalue Problems Testing example: testIQEP_Newton.m (uploaded in March 2008; last updated on July 15, 2016 by Ying Cui (cuiying@u.nus.edu)).

Some recent talks

• A majorized proximal point dual Newton algorithm for nonconvex statistical optimization problems (The Sixth International Conference on Continuous Optimization, Technical University (TU) of Berlin, Germany, August 3--8, 2019).
• Matrix Cones and Spectral Operators of Matrices (Advances in the Geometric and Analytic Theory of Convex Cones, Sungkyunkwan University, Korea, May 27--31, 2019).
• On the Relationships of ADMM and Proximal ALM for Convex Optimization Problems (Institute of Applied Physics and Computational Mathematics, Beijing, April 12, 2019).
• Sparse semismooth Newton methods and big data composite optimization (New Computing-Driven Opportunities for Optimization, Wuyishan, August 13-17, 2018).
• On the efficient computation of the projector over the Birkhoff polytope (International Symposium on Mathematical Programming 2018, Bordeaux, July 1-6, 2018)
• A block symmetric Gauss-Seidel decomposition theorem and its applications in big data nonsmooth optimization (International Workshop on Modern Optimization and Applications, AMSS, Beijing, June 16-18, 2018).
• On the Equivalence of Inexact Proximal ALM and ADMM for a Class of Convex Composite Programming (DIMACS Workshop on ADMM and Proximal Splitting Methods in Optimization, Rutgers University, June 11-13, 2018).
• A block symmetric Gauss-Seidel decomposition theorem and its applications in big data nonsmooth optimization (The Hong Kong Mathematical Society Annual General meeting 2018, May 26, 2018).
• SDPNAL+: A MATLAB software package for large-scale SDPs with a user-friendly interface (SIAM-ALA18, May 2018).
• Second order sparsity and big data optimization (October 2017).
• Error bounds and the superlinear convergence rates of the augmented Lagrangian methods (October 2017).
• Block symmetric Gauss-Seidel iteration and multi-block semidefnite programming (October 2017).
• A two-phase augmented Lagrangian approach for linear and convex quadratic semidefinite programming problems (December 2016).
• Linear rate convergence of the ADMM for multi-block convex conic programming (August 2016).
• An efficient inexact accelerated block coordinate descent method for least squares semidefinite programming (June 2015).
• Multi-stage convex relaxation approach for low-rank structured PSD matrix recovery (May 2014).

Some old talks

• An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP (April 2012).
• From linear programming to matrix programming: A paradigm shift in optimization (December 2011).
• A sequential convex programming approach for rank constrained matrix optimization problems (December 2011).
• Low rank matrix optimization problems: Back to nonconvex regularizations (June 2011).
• Matrix optimization: Searching between the first and second order methods (May 2011).
• A majorized penalty approach for calibrating rank constrained correlation matrix problems (October 2010).
• An introduction to a class of matrix cone programming (July 2010).
• A majoried penalty approach for calibrating rank constrained correlation matrix problems (July 2010).
• Rank constrained matrix optimization problems (May 2010).
• An Introduction to Correlation Stress Testing (March 2010).
• An Implementable Proximal Point Algorithmic Framework for Nuclear Norm Minimization (July 2009).
• A Proximal Point Method for Matrix Least Squares Problem with Nuclear Norm Regularization (May 2009).
• A Newton-CG Augmented Lagrangian Method for Large Sacle Semidefinite Programming (based on a revised version) (March 2009).
• A Newton-CG Augmented Lagrangian Method for Large Sacle Semidefinite Programming (October 2008).
• Calibrating least squares covariance matrix problems with equality and inequality constraints (July 2008).
• The Role of Metric Projectors in Nonlinear Conic Optimization (August 2007).
• Inverse Quadratic Eigenvalue Problems (July 2006).
• Recent Developments in Nonlinear Optimization Theory (July 2006).
• A short summer school course on modern optimization theory: optimality conditions and perturbation analysis Part I Part II Part III (July 2006).

Selected Publications

Click here for my google scholar page.

Click here for my ORCID page.

Technical Reports

Click here for the arXived

• Yan Gao and Defeng Sun, “A majorized penalty approach for calibrating rank constrained correlation matrix problems”, March 2010; PDF version MajorPen.pdf; Revised in May 2010; PDF version MajorPen_May5.pdf; See Rank_CaliMat.zip in the "MATLAB Codes" section for codes in Matlab.
• Jong-Shi Pang and Defeng Sun, “First-order sensitivity of linearly constrained strongly monotone composite variational inequalities”, December 2008.

2020—

· Xiangbin Hu, Jian Huang, Li Liu, Defeng Sun, and Xingqiu Zhao, “Subgroup analysis in the heterogeneous Cox model”, Statistics in Medicine (2020) XXX--XXX.

· Shujun Bi, Shaohua Pan, and Defeng Sun, “A multi-stage convex relaxation approach to noisy structured low-rank matrix recovery”, Mathematical Programming Computation 12 (2020) XXX--XXX.

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for linear programming”, SIAM Journal on Optimization 30 (2020) 2410--2440.

· Yangjing Zhang, Ning Zhang, Defeng Sun, and Kim Chuan Toh, “A proximal point dual Newton algorithm for solving group graphical Lasso problems”, SIAM Journal on Optimization 30 (2020) 2197--2220.

· Chao Ding, Defeng Sun, Jie Sun, and Kim Chuan Toh, “Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian”, SIAM Journal on Optimization 30 (2020) 630--659. [Revised from the second part of https://arxiv.org/abs/1401.2269, January 2014.]

· Liang Chen, Xudong Li, Defeng Sun, and Kim Chuan Toh, “On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming”, Mathematical Programming 18X (2020) [DOI:10.1007/s10107-019-01423-x] https://arxiv.org/pdf/1803.10803.pdf

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope”, Mathematical Programming 179 (2020) 419--446 [DOI: 10.1007/s10107-018-1342-9] https://arxiv.org/abs/1702.05934

· Yangjing Zhang, Ning Zhang, Defeng Sun, and Kim Chuan Toh, “An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems”, Mathematical Programming 179 (2020) 223--263 [DOI:10.1007/s10107-018-1329-6] https://arxiv.org/pdf/1712.05910.pdf

· Defeng Sun, Kim Chuan Toh, Yancheng Yuan, Xin-Yuan Zhao, “SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)”, Optimization Methods and Software 35 (2020) 87--115. [https://doi.org/10.1080/10556788.2019.1576176] https://arxiv.org/pdf/1710.10604.pdf

2019

· Ziyan Luo, Defeng Sun, Kim Chuan Toh, Naihua Xiu, “Solving the OSCAR and SLOPE models using a semismooth Newton-based augmented Lagrangian method”, Journal of Machine Learning Research 20(106):1--25, 2019.

· Liang Chen, Defeng Sun, Kim Chuan Toh, Ning Zhang, “A unified algorithmic framework of symmetric Gauss-Seidel decomposition based proximal ADMMs for convex composite programming”, Journal of Computational Mathematics 37 (2019) 739--757.

· Shenglong Hu, Defeng Sun, Kim Chuan Toh, “Best nonnegative rank-one approximations of tensors”, SIAM Journal on Matrix Analysis and Applications 40 (2019) 1527--1554.

· Ying Cui, Defeng Sun, Kim Chuan Toh, “Computing the best approximation over the intersection of a polyhedral set and the doubly nonnegative cone”, SIAM Journal on Optimization 29 (2019) 2785--2813.

· Meixia Lin, Yong-Jin Liu, Defeng Sun, Kim Chuan Toh, “Efficient sparse semismooth Newton methods for the clustered lasso problem”, SIAM Journal on Optimization 29 (2019) 2026--2052.

· Liang Chen, Defeng Sun, Kim Chuan Toh, “Some problems on the Gauss-Seidel iteration method in degenerate cases”, Journal on Numerical Methods and Computer Applications, 40 (2019) 98--110 (in Chinese)

· Ying Cui and Defeng Sun, and Kim Chuan Toh, “On the R-superlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming”, Mathematical Programming 178 (2019) 381--415 [DOI: 10.1007/s10107-018-1300-6] https://arxiv.org/abs/1706.08800

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications”, Mathematical Programming 175 (2019) 395--418. arXiv:1703.06629

Theses of Students:

• “Simultaneous Model for Clustering and Intra-Group Feature Selection”, (PhD thesis of Yuan Yancheng, supervisor during August 2015-July 2018, NUS) August 2019.
• “Efficient Hessian Based Algorithms for Solving Sparse Group Lasso and Multiple Graphical Lasso Problems”, (PhD thesis of ZHANG Yangjing, supervisor during August 2014-July 2018, NUS) January 2019.
• “Practical Algorithms for Large Scale Convex Composite Conic Programming Problem”, (PhD thesis of LAM Xin Yee, co-supervisor during August 2014-July 2018, NUS) February 2019.

2018

· Yancheng Yuan, Defeng Sun and Kim Chuan Toh, “An efficient semismooth Newton based algorithm for convex clustering”, Proceedings of the 35-th International Conference on Machine Learning (ICML), Stockholm, Sweden, PMLR 80, 2018.

· Xin Yee Lam, J.S. Marron, Defeng Sun, and Kim Chuan Toh, “Fast algorithms for large scale generalized distance weighted discrimination”, Journal of Computational and Graphical Statistics 27 (2018) 368--379. arXiv:1604.05473.

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming”, Mathematical Programming Computation, 10 (2018) 703--743. https://arxiv.org/pdf/1512.08872.pdf

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “On efficiently solving the subproblems of a level-set method for fused lasso problems”, SIAM Journal on Optimization 28 (2018) 1842--1862. https://arxiv.org/abs/1512.08872

· Deren Han, Defeng Sun, and Liwei Zhang, “Linear rate convergence of the alternating direction method of multipliers for convex composite programming’’, Mathematics of Operations Research 43 (2018) 622--637. [Revised from the first part of arXiv:1508.02134, August 2015.]

· Chao Ding, Defeng Sun, Jie Sun, and Kim Chuan Toh, “Spectral operators of matrices”, Mathematical Programming 168 (2018) 509--531. [Revised from the first part of https://arxiv.org/abs/1401.2269, January 2014.]

· Ying Cui and Defeng Sun, “A complete characterization on the robust isolated calmness of the nuclear norm regularized convex optimization problems”, Journal of Computational Mathematics 36(3) (2018) 441--458.

· Xudong Li, Defeng Sun, and Kim Chuan Toh, “A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems’’, SIAM Journal on Optimization 28 (2018) 433--458.

[ This paper brought Xudong Li the Best Paper Prize for Young Researchers in Continuous Optimization announced in the ICCOPT 2019 held in Berlin, August 3-8, 2019. This is the only prize given in the flagship international conference on continuous optimization held every three years].

Theses of Students:

• “EFFICIENT DUALITY-BASED NUMERICAL METHODS FOR SPARSE PARABOLIC OPTIMAL CONTROL PROBLEMS”, (PhD thesis of CHEN Bo, NUS) June 2018.

2017

· Chao Ding, Defeng Sun, and Liwei Zhang, “Characterization of the robust isolated calmness for a class of conic programming problems”, arXiv:1601.07418. SIAM Journal on Optimization 27 (2017) 67--90.

· Liang Chen, Defeng Sun, and Kim Chuan Toh, “A note on the convergence of ADMM for linearly constrained convex optimization problems”, arXiv:1507.02051. Computational Optimization and Applications 66 (2017) 327--343. [In this note a comprehensive proof is supplied to clarify many ambiguities/incorrect proofs in the literature].

· Liang Chen, Defeng Sun, and Kim Chuan Toh, “An efficient inexact symmetric Gauss-Seidel based majorized ADMM for high-dimensional convex composite conic programming”, arXiv:1506.00741. Mathematical Programming 161 (2017) 237--270.

Theses of Students:

• “The Metric Subregularity of KKT Solution Mappings of Composite Conic Programming”, (PhD thesis of GUO Han) March 2017.

2016

• Ying Cui, Chenlei Leng, and Defeng Sun, “Sparse estimation of high-dimensional correlation matrices”, Computational Statistics & Data Analysis Vol. 93 (2016) 390–403.
• Defeng Sun, Kim Chuan Toh, and Liuqin Yang, “An efficient inexact ABCD method for least squares semidefinite programming”, May 2015, SIAM Journal on Optimization 26 (2016) 1072--1100. Detailed computational results for over 600 problems tested in the paper.
• Jin Qi, Melvyn Sim, Defeng Sun, and Xiaoming Yuan, “Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium”, September 2010, Transportation Research Part B 94 (2016) 264--284.
• Ying Cui, Xudong Li, Defeng Sun, and Kim Chuan Toh, “On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions”( Dedicated to Professor Lucien Polak on the occasion of his 85th birthday), February 2015, Journal of Optimization Theory and Applications 169 (2016) 1013--1041.
• Min Li, Defeng Sun, and Kim Chuan Toh, “A majorized ADMM with indefinite proximal terms for linearly constrained convex composite optimization”, December 2014, SIAM Journal on Optimization 26 (2016) 922--950.
• Weimin Miao, Shaohua Pan, and Defeng Sun, “A rank-corrected procedure for matrix completion with fixed basis coefficients’’, Mathematical Programming 159 (2016) 289--338.
• Caihua Chen, Yong-Jin Liu, Defeng Sun, and Kim Chuan Toh, “A semismooth Newton-CG dual proximal point algorithm for matrix spectral norm approximation problems’’, November 2012, Mathematical Programming 155 (2016) 435–470.
• Xudong Li, Defeng Sun, and Kim Chuan Toh, “A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions’’, arXiv:1409.2679, arXiv:1409.2679, Mathematical Programming 155 (2016) 333-373. You may find the detailed comparisons here.

Theses of Students:

• “Large Scale Composite Optimization Problems with Coupled Objective Functions: Theory, Algorithms and Applications”, (PhD thesis of CUI Ying) January 2016. [Her dissertation was awarded the Louis Chan Hsiao Yun Best Dissertation Prize by the National University of Singapore in 2018]

2015

• Liuqin Yang, Defeng Sun, and Kim Chuan Toh, “SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints”, Mathematical Programming Computation Vol. 7, Issue 3 (2015) 331–366. Detailed computational results for over 500 problems tested in the paper. [This paper together with the accompany software was awarded the triennial Beale–Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society at Bordeaux, France, July 2-6, 2018. See Picture 1, Picture 2, and Picture 3.]
• Min Li, Defeng Sun, and Kim Chuan Toh, “A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block’’, arXiv:1410.7933, arXiv:1410.7933, Asia-Pacific Journal of Operational Research 32 (2015) 1550024 (19 pages).
• Defeng Sun, Kim Chuan Toh, and Liuqin Yang, “A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type constraints”, SIAM Journal on Optimization Vol. 25, No. 2 (2015) 882–915. Detailed computational results for over 400 problems tested in the paper. You may also find a supplementary note here on more detailed comparisons between the performance of our proposed algorithm and various variants of ADMMs.

Theses of Students:

• “An inexact Alternating Direction Method of Multipliers for Convex Composite Conic Programming with Nonlinear Constraints”, (PhD thesis of DU Mengyu) August 2015.
• “A Two-Phase Augmented Lagrangian Method for Convex Composite Quadratic Programming”, (PhD thesis of LI Xudong) January 2015.

2014

• Kaifeng Jiang, Defeng Sun, and Kim Chuan Toh, “A partial proximal point algorithm for nuclear norm regularized matrix least squares problems”, PDF version Mathematical Programming Computation 6 (2014) 281--325.
• Chao Ding, Defeng Sun, and Jane Ye, “First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints”, November 2010, PDF version SDCMPCC-Nov-15.pdf; Revised in May 2012; PDF version SDCMPCC_Revised_May16_12; online version SDCMPCC_online.pdf Mathematical Programming 147 (2014) 539-579.
• Bin Wu, Chao Ding, Defeng Sun, and Kim Chuan Toh, “On the Moreau-Yosida regularization of the vector k-norm related functions”, PDF version SIAM Journal on Optimization 24 (2014) 766--794.
• Chao Ding, Defeng Sun, and Kim Chuan Toh, “An introduction to a class of matrix cone programming”, PDF version. Mathematical Programming 144 (2014) 141-179.

Theses of Students:

• “A General Framework for Structure Decomposition in High-Dimensional Problems”, Thesis_YangJing.pdf (Master thesis of YANG Jing) August 2014.
• “Sparse Coding Based Image Restoration and Recognition: Algorithms and Analysis”, Thesis_BaoChenglong.pdf (PhD thesis of BAO Chenglong) August 2014.
• “High-Dimensional Analysis on Matrix Decomposition with Application to Correlation Matrix Estimation in Factor Models”, Thesis_WuBin.pdf (PhD thesis of WU Bin) January 2014.

2013

• Maryam Fazel, Ting Kei Pong, Defeng Sun, and Paul Tseng, “Hankel matrix rank minimization with applications to system identification and realization”, Hankel-Matrix-semi-Proximal-ADMM SIAM Journal on Matrix Analysis and Applications 34 (2013) 946-977.
• Junfeng Yang, Defeng Sun, and Kim Chuan Toh, “A proximal point algorithm for log-determinant optimization with group lasso regularization”, GROUP LASSO REGULARIZATION.pdf SIAM Journal on Optimization 23 (2013) 857--893.
• Kaifeng Jiang, Defeng Sun, and Kim Chuan Toh, “Solving nuclear norm regularized and semidefinite matrix least squares problems with linear equality constraints”, PDF version PPA_Semismooth-Revision.pdf. Fields Institute Communications Series on Discrete Geometry and Optimization, K. Bezdek, Y. Ye, and A. Deza eds., 2013.

Theses of Students:

• “Matrix Completion Models with Fixed Basis Coefficients and Rank Regularized Problems with Hard Constraints”, PhDThesis_Miao_Final.pdf (PhD thesis of MIAO Weimin) January 2013.

2012

• Kaifeng Jiang, Defeng Sun, and Kim Chuan Toh, “An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP”, iAPG_QSDP.pdf SIAM Journal on Optimization 22 (2012) 1042--1064. [The algorithm is used in NAG’s nearest correlation library]
• Yong-Jin Liu, Defeng Sun, and Kim Chuan Toh, “An implementable proximal point algorithmic framework for nuclear norm minimization”, July 2009, PDF version Nucnorm_July13.pdf;Revised in March 2010, PDF version Nucnorm-16Mar10.pdf; Revised in October 2010, PDF version Nucnorm-02Oct10.pdf; Mathematical Programming 133 (2012) 399-436. See the "MATLAB Codes" section for codes in Matlab.

Theses of Students:

• “Numerical Algorithms for a Class of Matrix Norm Approximation Problems”, PDF version Chen Caihua_Thesis_final.pdf (PhD thesis of former visiting student Caihua Chen from Nanjing University) June 2012.
• “An Introduction to A Class of Matrix Optimization Problems”, PDF version DingChao_Thesis_final.pdf (PhD thesis of DING Chao) January 2012.

2011

• Houduo Qi and Defeng Sun, “An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem”, PDF version CorrMatHnorm.pdf; IMA Journal of Numerical Analysis 31 (2011) 491--511. See the "MATLAB Codes" section for codes in Matlab.

2010

• Chengjing Wang, Defeng Sun, and Kim Chuan Toh, “Solving log-determinant optimization problems by a Newton-CG proximal point algorithm”, September 2009, PDF version logdet-NAL-29Sep09.pdf; Revised in March 2010, PDF version logdet-NAL-12Mar10.pdf; SIAM Journal on Optimization 20 (2010) 2994--3013. See the "MATLAB Codes" section for codes in Matlab.
• Xinyuan Zhao, Defeng Sun, and Kim Chuan Toh, “A Newton-CG augmented Lagrangian method for semidefinite programming”, PDF version NewtonCGAugLag.pdf ; SIAM Journal on Optimization 20 (2010) 1737--1765. See the "MATLAB Codes" section for codes in Matlab.
• Houduo Qi and Defeng Sun, “Correlation stress testing for value-at-risk: an unconstrained convex optimization approach”, PDF version stress_test.pdf; Computational Optimization and Applications 45 (2010) 427--462. See the "MATLAB Codes" section for codes in Matlab.

Theses of Students:

• “Structured Low Rank Matrix Optimization Problems: A Penalized Approach” PDF version main_gy.pdf (PhD thesis of GAO Yan) August 2010.

2009

• Yan Gao and Defeng Sun, “Calibrating least squares covariance matrix problems with equality and inequality constraints”, PDF version CaliMat.pdf; SIAM Journal on Matrix Analysis and Applications 31 (2009) 1432--1457. See the "MATLAB Codes" section for codes in Matlab.

Theses of Students:

• “A Semismooth Newton-CG Augmented Lagrangian Method for Large Scale Linear and Convex Quadratic SDPs” PDF version main_xyz.pdf (PhD thesis of ZHAO Xinyuan) August 2009. [See the "MATLAB Codes" section for the software for solving linear SDPs.]
• “A Study on Nonsymmetric Matrix-Valued Functions” PDF version Main_YZ.pdf (Master thesis of YANG Zhe) August 2009.

2008

• Jiri Outrata and Defeng Sun, “On the coderivative of the projection operator onto the second order cone”, Set-Valued Analysis 16 (2008) 999--1014.
• Zi Xian Chan and Defeng Sun, “Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming”. Final PDF version SiamCS07.pdf SIAM Journal on Optimization 19 (2008) 370--396. [This project brought the inaugural outstanding undergraduate researcher prize at National University of Singapore in AY 2006/07 to Zi Xian]
• J.-S. Chen, Defeng Sun, and Jie Sun, “The SC^1 property of the squared norm of the SOC Fischer-Burmeister function”. PDF file lipschitz_ORL_10_07.pdf Operations Research Letters 36 (2008) 385--392.
• Defeng Sun and Jie Sun, “Loewner's operator and spectral functions in Euclidean Jordan algebras”. Final PDF version MOR_SS4.pdf Mathematics of Operations Research 33 (2008) 421--445.
• Defeng Sun, Jie Sun, and Liwei Zhang, “The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming”. Mathematical Programming 114 (2008) 349--391.

2007

• Zheng-Jian Bai, Delin Chu, and Defeng Sun, “A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure”. SIAM Journal on Scientific Computing 29 (2007) 2531--2561. [This paper brought Zheng-Jian Bai the The Applied Numerical Algebra Prize in the Second International Conference on Numerical Algebra and Scientific Computing (NASC 2008)].

2006

• Defeng Sun, “The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications”, Final PDF version NLSDP_Final.pdf Mathematics of Operations Research 31 (2006) 761--776.
• Houduo Qi and Defeng Sun, “A quadratically convergent Newton method for computing the nearest correlation matrix”, SIAM Journal on Matrix Analysis and Applications 28 (2006) 360--385. Code in Matlab [The algorithm is used in NAG’s nearest correlation library]
• Zheng-Hai Huang, Defeng Sun and Gongyun Zhao, “A smoothing Newton-type algorithm of stronger convergence for the quadratically constrained convex quadratic programming”, Revised PDF version HSZ_Re.pdf Computational Optimization and Applications 35 (2006) 197--237.

2005

• Fanwen Meng, D.F. Sun and Gongyun Zhao, “Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization”, Mathematical Programming 104 (2005) 561--581.
• D.F. Sun and Jie Sun, “Nonsmooth Matrix Valued Functions Defined by Singular Values”, December 2002. PDF version SS3.pdf. Revised with the new title as “Strong semismoothness of Fischer-Burmeister SDC and SOC functions”, Final PDF version SS3_Rev.pdf Mathematical Programming 103 (2005) 575--581.
• D. Han, Xun Li, D.F. Sun, and Jie Sun, “Bounding option prices of multi-assets: a semidefinite programming approach”, PDF version HLSS.pdf Pacific Journal of Optimization 1 (2005) 59--79. (Special issue in honor of the 70th birthday of R Tyrrell Rockafellar).

Theses of Students:

• “Smoothing Approximations for Two Classes of Convex Eigenvalue Optimization Problems” PDF version Yu_Aug_2005.pdf (Master thesis of YU Qi)
• “A Smoothing Newton Method for the Boundary-Valued ODEs” PDF version Zheng_May_2005.pdf (Master thesis of ZHENG Zheng)

2004

• Z. Huang, L. Qi and D.F. Sun, “Sub-Quadratic Convergence of a Smoothing Newton Algorithm for the P_0-- and Monotone LCP”, PDF version hqs_revised_Feb20.pdf Mathematical Programming, 99 (2004), 423--441.
• Jie Sun, D.F. Sun and L. Qi, “A Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems”, Final version SSQ_Oct15.pdf SIAM Journal on Optimization, 14 (2004), 783--806.

Theses of Students:

• “Smooth Convex Approximation and Its Applications” PDF version Shi_July_2004.pdf (Master thesis of Shengyuan SHI)
• “The Smoothing Function of the Nonsmooth Matrix Valued Function” PDF version Zhao_July_2004.pdf (Master thesis of Jinye ZHAO)

2003

• H.-D. Qi, L. Qi and D.F. Sun, “Solving KKT Systems via the Trust Region and the Conjugate Gradient Methods,” SIAM Journal on Optimization, 14 (2003) 439--463.
• J.S. Pang, D.F. Sun and Jie Sun, “Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Cone Complementarity Problems,” PDF version PSS_03.pdf Mathematics of Operations Research, 28 (2003) 39-63.
• X.D. Chen, D. Sun and Jie Sun, “Complementarity Functions and Numerical Experiments for Second-Order-Cone Complementarity Problems,” PDF version coap_03.pdf Computational Optimization and Applications, 25 (2003) 39 -- 56.
• G. Zhou, Kim Chuan Toh, and Defeng Sun, “Semismooth Newton methods for minimizing a sum of Euclidean norms with linear constraints,” Postscript version zts.ps PDF version zts.pdf. Journal of Optimization Theory and Applications, 119 (2003), 357--377.
• D.F. Sun and Jie Sun, “Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems,” SIAM Journal on Numerical Analysis, 40 (2003) 2352--2367.

2002

• D.F. Sun, R.S. Womersley and H.-D. Qi, “A feasible semismooth asymptotically Newton method for mixed complementarity problems”, PDF version SWQ_02.pdf Mathematical Programming, 94 (2002) 167--187.
• D.F. Sun and Jie Sun, “Semismooth Matrix Valued Functions”, PDF version SS_02.pdf Mathematics of Operations Research, 27 (2002) 150--169.
• L. Qi and D. Sun, “Smoothing Functions and a Smoothing Newton Method for Complementarity and Variational Inequality Problems”, Journal of Optimization Theory and Applications, 113 (2002) 121--147.
• L. Qi, D. Sun and G. Zhou, ``A primal-dual algorithm for minimizing a sum of Euclidean norms'', Journal of Computational and Applied Mathematics, 138 (2002) 127--150.

2001

• D. Sun, “A further result on an implicit function theorem for locally Lipschitz functions”, PDF version implicit.pdf Operations Research Letters, 28 (2001) 193--198.
• D. Sun and L. Qi, “Solving variational inequality problems via smoothing-nonsmooth reformulations”, PDF version proj_smooth.pdf Journal of Computational and Applied Mathematics, 129 (2001) 37--62.
• Y.B. Zhao and D. Sun, “Alternative theorems for nonlinear projection equations and their applications to generalized complementarity problems”, Nonlinear Analysis: Theory, Methods and Applications. 46 (2001) 853--868.
• L. Qi and D. Sun, “Nonsmooth & Smoothing Methods for NCP & VI”, the Encyclopedia of Optimization , C. Floudas and P. Pardalos (editors), (Kluwer Academic Publisher, Nowell, MA. USA, 2001) 100-104.
• E. Polak, L. Qi and D. Sun, "Second-Order Algorithms for Generalized Finite and Semi-Infinite Min-Max Problems," SIAM Journal on Optimization 11 (2001) 937--961.

2000

• L. Qi, D. Sun and G. Zhou, “A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities,” Mathematical Programming, 87 (2000), 1--35.
• L. Qi and D. Sun, ``Improving the convergence of non-interior point algorithms for nonlinear complementarity problems'', Mathematics of Computation, 69 (2000), 283--304.
• Y. Dai, J. Han, G. Liu, D. Sun, H. Yin and Y. Yuan, “Convergence properties of nonlinear conjugate gradient methods,” SIAM Journal on Optimization, 10 (2000), 345--358.
• L. Qi and D. Sun, “Polyhedral methods for solving three index assignment problems,” Nonlinear Assignment Problems: Algorithms and Applications, P.M. Pardalos and L. Pitsoulis, eds., (Kluwer Academic Publisher, Nowell, MA, USA, 2000), 91--107.

1999

• R. Mifflin, L. Qi and D. Sun, “Properties of Moreau-Yosida regularization of a piecewise $C^2$ convex function,” Mathematical Programming, Vol. 84, 1999, 269--281.
• D. Sun and R. S. Womersley, “A New Unconstrained Differentiable Merit Function for Box Constrained Variational Inequality Problems and a Damped Gauss-Newton Method,” PDF version Sun_Womersley_99.pdf SIAM Journal on Optimization, Vol. 9, 1999, pp. 409--434.
• E. Polak, L. Qi and D. Sun, “First-Order Algorithms for Generalized Finite and Semi-Infinite Min-Max Problems,” Computational Optimization and Applications, Vol. 13, pp. 137-161, 1999.
• D. Sun and L. Qi, “On NCP functions,” PDF version ncp.pdf Computational Optimization and Applications, Vol. 13, 1999, 201--220.
• D. Sun, “A regularization Newton method for solving nonlinear complementarity problems,” PDF version AMO_99.pdf Applied Mathematics and Optimization, 40 (1999), 315-339.
• L. Qi and D. Sun, “A survey of some nonsmooth equations and smoothing Newton methods,” PDF version qsreview1.pdf in Andrew Eberhard, Barney Glover, Robin Hill and Daniel Ralph eds., Progress in optimization, 121--146, Appl. Optim., 30, Kluwer Acad. Publ., Dordrecht, 1999.
• G. Zhou, D. Sun and L. Qi, “Numerical experiments for a class of squared smoothing Newton methods for complementarity and variational inequality problems,” PDF version zsq_99.pdf in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi (eds.), Kluwer Academic Publishers B.V., 421--441, 1999.

1998

• F. Potra, L. Qi and D. Sun, “Secant methods for semismooth equations,” Numerische Mathematik, Vol. 80, 1998, 305--324.
• X. Chen, L. Qi and D. Sun, “Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities,” Mathematics of Computation, 67 (1998), pp. 519-540.
• R. Mifflin, D. Sun and L. Qi, “Quasi-Newton bundle-type methods for nondifferentiable convex optimization,” SIAM Journal on Optimization, Vol. 8, 1998, 583 - 603.
• H. Jiang, M. Fukushima, L. Qi and D. Sun, “A trust region method for solving generalized complementarity problems,” SIAM Journal on Optimization, Vol. 8, 1998, pp. 140-157.
• J. Han and D.F. Sun, “Newton-Type methods for variational inequalities,” Advances in Nonlinear Programming, Y. Yuan eds, Klumer, Boston, 1998, pp. 105 -- 118.
• D.F. Sun and J. Han and Y.B. Zhao, “On the finite termination of the damped-Newton algorithm for the linear complementarity problem,” Acta Mathematica Numerica Applicatae, Vol. 21:1, 1998, 148--154.

1997

• D. Sun and J. Han, “Newton and quasi-Newton methods for a class of nonsmooth equations and related problems,” PDF version Sun_Han_97.pdf SIAM Journal on Optimization, 7 (1997) 463--480.
• D. Sun, M. Fukushima and L. Qi, “A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problem,” PDF version SFQ_97.pdf in: M.C. Ferris and J.-S. Pang, eds., Complementarity and Variational Problems -- State of the Art, SIAM Publications, Philadelphia, 1997, pp. 452-473.
• J. Han and D. Sun, “Newton and quasi-Newton methods for normal maps with polyhedral sets,” Journal of Optimization Theory and Applications, Vol. 94, No. 3, pp. 659-676, September 1997.
• D. Sun and J. Han, “On a conjecture in Moreau-Yosida approximation of a nonsmooth convex function”, Chinese Science Bulletin 42 (1997) 1423--1426.

1996

• D. Sun, “A class of iterative methods for solving nonlinear projection equations”, Journal of Optimization Theory and Applications, Vol. 91, No.1, 1996, pp. 123--140.
• H. Jiang, L. Qi, X. Chen and D. Sun, ``Semismoothness and Superlinear Convergence in Nonsmooth Optimization and Nonsmooth Equations'', Nonlinear Optimization and Applications, G. Di Pillo and F. Giannessi eds., (Plenum Publishing Corporation, New York), 1996, 197--212.

1995

• G. Liu, J. Han and D. Sun, “Global convergence of BFGS method with nonmonotone line search”, Optimization 34 (1995) 147--159.
• D. Sun, “A new step-size skill for solving a class of nonlinear projection equations”, Journal of Computational Mathematics 13:4 (1995), 357--368.

• D. F. Sun, Algorithms and Convergence Analysis for Nonsmooth Optimization and Nonsmooth Equations, PhD thesis (submitted in December 1994 and defended in March 1995), Institute of Applied Mathematics, Chinese Academy of Sciences.

1994

• D. Xu and D. Sun, “A modification of successive approximation method for nonsmooth equations”, PDF version Xu_Sun_smoothing_94.pdf Qufu Shifan Daxue Xuebao Ziran Kexue Ban 20:3 (1994) 14--20.
• D. Sun and J. Wang, “An approximation method for stochastic programming with recourse”, Mathematica Numerica Sinica 16 (1994) 80--92. (In Chinese). English translation published in Chinese Journal of Numerical Mathematics and Applications 16:2 (1994) 70--83.
• D. Sun, “A projection and contraction method for the nonlinear complementarity problem and its extensions'', PDF version Sun94.pdf Mathematica Numerica Sinica 16 (1994) 183--194. (In Chinese). English translation published in Chinese Journal of Numerical Mathematics and Applications 16:3 (1994) 73--84.
• D.F. Sun, “An iterative method for solving variational inequality problems and complementarity problems”, Numerical Mathematics A Journal of Chinese Universities 16 (1994) 145--153. (In Chinese).

1993

D.F. Sun, “Projected extragradient method for finding saddle points of general convex programming”', Qufu Shifan Daxue Xuebao Ziran Kexue Ban 19:4 (1993) 10--17.

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Last Modified: September 30, 2020
Defeng Sun, Department of Applied Mathematics, The Hong Kong Polytechnic University