Welcome
to Defeng Sun's Home Page
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 [Supervisor:
Professor Jiye
Han (韩继业)]
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 including
real-world applications 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. You may also want to know the Hong Kong PhD
Fellowship Scheme.
- Research
Assistants/Research Fellows/Postdoctoral Fellows: multiple positions are available immediately;
working on various projects about Convex and Non-Convex Optimization,
Optimal Control, Optimal Transport, Software Development and others.
Priority will be given to those who have some computational
experience.
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 and Relocated at 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 an inaugural CSIAM Fellow
in 2020
by the China Society for Industrial and
Applied Mathematics.
- Elected a SIAM
Fellow in 2020
by the Society for Industrial and Applied
Mathematics.
- 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
[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.]
[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]
[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
[Peipei Tang, Chengjing
Wang, Defeng Sun, and Kim Chuan Toh, “A sparse semismooth Newton based proximal majorization-minimization
algorithm for nonconvex square-root-loss regression problems”, Journal of
Machine Learning Research 21(226):1--38, 2020.]
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
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
Selected
Publications
Click here
for my google scholar page.
Click here
for my ORCID page.
Technical Reports
Click here
for the arXived
2021—
·
Ran Yan, Shuaian
Wang, Jiannong Cao,
and Defeng Sun, “ Shipping
Domain Knowledge Informed Prediction and
Optimziation in Port State Control”, Transportation
Research Part B 149
(2021) 52--78.
·
Defeng Sun,
Kim Chuan Toh, and Yancheng
Yuan, “Convex clustering: Model, theoretical guarantee and
efficient algorithm”, Journal of Machine Learning
Research 22(9):1−32,
2021. arXiv:1809.04249
·
Ling Liang, Defeng Sun, and Kim Chuan Toh,
“An inexact augmented Lagrangian
method for second-order cone programming with applications”, SIAM Journal on Optimization 31 (2021).
·
Xin Yee Lam, Defeng
Sun, and Kim Chuan Toh, “A
semi-proximal augmented Lagrangian based decomposition method for primal block
angular convex composite quadratic conic programming problems”, INFORMS Journal on
Optimization 3 (2021) XXX--XXX. arXiv:1812.04941
·
Ning Zhang, Yangjing Zhang, Defeng
Sun, and Kim Chuan Toh,
“An efficient linearly
convergent regularized proximal point algorithm for fused multiple graphical
Lasso problems”,
SIAM Journal on
Mathematics of Data Science 3 (2021) 524--543.
·
Lei
Yang, Jia Li, Defeng Sun, and Kim Chuan Toh, “A fast globally
linearly convergent algorithm for the computation of Wasserstein barycenters”,
Journal
of Machine Learning Research 22(21):1−37, 2021.
arXiv:1809.04249
·
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 185 (2021) 111—161.
2020
·
Peipei Tang, Chengjing Wang, Defeng Sun, and Kim Chuan Toh, “A sparse semismooth Newton based proximal
majorization-minimization algorithm for nonconvex square-root-loss regression
problems”, Journal of Machine Learning
Research 21(226):1--38, 2020. [See the software package square_root_PMM]
·
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) 569--602.
·
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.]
·
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.
·
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.
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:
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:
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:
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:
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:
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:
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
2006
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:
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”, SIAM Journal on Optimization, 14 (2004), 783--806.
Theses of Students:
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”, Operations
Research Letters, 28 (2001) 193--198.
- D. Sun and L. Qi, “Solving
variational inequality problems via smoothing-nonsmooth reformulations”, 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
1994
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.
Return to: Department
of Applied Mathematics, The Hong Kong
Polytechnic University
Last Modified: May 14, 2021
Defeng Sun, Department of Applied Mathematics, The Hong Kong Polytechnic
University