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 730, Yip Kit Chuen
Building
Phone: +852 2766 6935
Fax:
+852 2362
9045
Email: defeng.sun@polyu.edu.hk
Web: http://www.mypolyuweb.hk/~dfsun/
Brief
History
Born in a small village (where
the story of Mo Yan’s award winning novel Red Sorghum took
place) located at Gaomi County (高密縣), Shandong Province, China.
BSc (1989) from Nanjing University, China,
majoring in Computational Mathematics; MSc (1992) also from Nanjing University, working on Variational
Inequalities under the supervision of Professor Bingsheng He and Stochastic Optimization
under the supervision of Professor Jinde Wang;
PhD (1995) from Institute of Applied
Mathematics, Chinese Academy of Sciences under the supervision of Professor
Jiye Han
focusing on Nonsmooth Equations and Optimization; Visiting Fellow, Research
Associate and then Australian Postdoctoral Fellow, the University of New South Wales, Australia
(1995--2000) all working in the area of Optimization; Assistant Professor
(December 2000--December 2005)/Associate
Professor (January 2006--June 2009)/Professor (July 2009--) at Department of Mathematics, National
University of Singapore. I also worked for Risk Management
Institute (RMI) as Deputy Director, Research (August 2009--August 2014) and
its acting program director to Masters of Financial Engineering (March--June,
2014). I joined The Hong Kong
Polytechnic University on August 1, 2017 as Chair Professor of Applied
Optimization and Operations Research at Department
of Applied Mathematics.
Recent
Research Interests
- Matrix Optimization (MatOpt): Theory,
Algorithms, Software and Applications
- Sparse
Newton Methods with Low Complexities
- High-Dimensional
Statistical Optimization
- Second Order Variational Analysis
- Risk Management and Computational Finance
Teaching
- AMA502 Operations Research
Methods
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.
Professional
Activities
- 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--).
- Editor-in-chief, Asia-Pacific Journal of
Operational Research (October 2010 –December 2013).
Advisory Committee Member from January 2014.
- Associate Editor, Science
China Mathematics (January 2018 --).
- Society Membership: INFORMS,
SIAM, MOS,
and etc.
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 January 31, 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.m
(for win64 operating system) and if use win32 or Linux system, you need to
download the installmex file installmex.m and
the c-file mexedig.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 (trial version) was
written by Ying Cui (yingcui@usc.edu)
and the code in Python CorrelationMatrix.py
(trial version) was written by Yancheng Yuan (e0009066@u.nus.edu),
respectively. (Updated on May 11, 2017).
- 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).
- 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
- SDPNAL+: a
MATLAB software for solving large scale semidefinite programming with
bound constraints [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.]
[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 K.C. 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].
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
- 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
2019--
·
Meixia Lin, Yong-Jin Liu, Defeng Sun, Kim Chuan Toh, “Efficient
sparse Hessian based algorithms for the clustered lasso problem”, SIAM Journal on Optimization (2019) https://arxiv.org/abs/1808.07181
·
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 (2019)
·
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
(2019) (in Chinese)
·
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 (2019) [https://doi.org/10.1080/10556788.2019.1576176] https://arxiv.org/pdf/1710.10604.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
17X (2019) 1--28 [DOI:
10.1007/s10107-018-1342-9] https://arxiv.org/abs/1702.05934
·
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 17X (2019) 1--29
[DOI: 10.1007/s10107-018-1300-6] https://arxiv.org/abs/1706.08800
·
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 17X (2019) 1--41
[DOI:10.1007/s10107-018-1329-6] https://arxiv.org/pdf/1712.05910.pdf
·
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
2018
·
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
·
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.
·
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
·
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.
·
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.]
·
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. (an earlier
shorter version https://arxiv.org/abs/1607.05428v1).
·
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.
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
- 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.
- Ying Cui, Chenlei
Leng, and Defeng Sun, “Sparse
estimation of high-dimensional correlation matrices”, Computational Statistics & Data
Analysis Vol. 93 (2016) 390–403.
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.
- 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.
- Yong-Jin Liu, Defeng Sun, and K. C. 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 K. C. 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 K. C. 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” Final PDF version singapore4.pdf 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”. PDF version
BCS-IQEP_rev.pdf SIAM Journal on Scientific Computing 29 (2007)
2531--2561.
2006
2005
- Fanwen Meng, D.F. Sun and Gongyun Zhao ,
“Semismoothness of solutions to generalized equations and the
Moreau-Yosida regularization”, Final PDF version
MSZ_May_05.pdf Mathematical Programming 104 (2005) 561--581.
- D.F. Sun and J. 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 J. 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.
- J. 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:
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 J. 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 J. 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, K.
C. 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 J. 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 J. 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,” PDF version QSZ_00.pdf
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,” PDF
version CQS_98.pdf 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. Sun, “Newton-Type methods for variational
inequalities,” Advances in Nonlinear Programming, Y. Yuan eds,
Klumer, Boston, 1998, pp. 105 -- 118.
- D. 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. 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: February 11, 2019
Defeng Sun, Department of Applied Mathematics, The Hong Kong Polytechnic
University