Welcome to Defeng Sun's Home Page
Office:
S17, #08-03
Phone:
+65 6516 3343
Fax:
+65 6779 5452
Email:
[matsundf@nus.edu.sg] or [matsundf@math.nus.edu.sg]
Mail:
Department of
Mathematics
National University of Singapore
10 Lower Kent Ridge Road
Singapore 119076, Republic of Singapore
Brief
History
Born in Gaomi County, 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;
I have been with Department of
Mathematics, National University of Singapore since December 2000 as
Assistant Professor (--December 2005)/Associate Professor (January 2006--June
2009)/Professor (July 2009--). 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).
Recent
Research Interests
- Matrix Optimization (MatOpt):
Theory, Algorithms, Software and Applications
- Variational Analysis and
Complementarity System
- Nonsmooth Matrix Analysis and
Computations
- High-Dimensional Statistical
Optimization
- Computational Finance: Financial Optimization
- Risk Management: Correlation stress test
Teaching
- 2015/2016, Semester I,
MA4260 Stochastic Operations Research
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. Any exceptional student with/without
TOEFL/GRE scores will be considered. Drop me an email to check if I am
qualified to be your supervisor. For information about my optimization
colleagues working at mathematics department, please visit their websites
here Pang Chin How, Jeffrey , Kim Chuan TOH and Gongyun
ZHAO .
Professional
Activities
Codes
in Matlab and others
Codes
for nearest (covariance) correlation matrix problems
- Codes for the Nearest Correlation Matrix problem: CorrelationMatrix.m
is a Matlab code written for computing the
nearest correlation matrix problem (uploaded in August 2006; last updated
on March 16, 2016). 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 (cuiying@u.nus.edu)
and the code in Python CorrelationMatrix.py (trial version) was
written by Yancheng Yuan (e0009066@u.nus.edu),
respectively, both from National
University of Singapore. (Updated on March 19, 2016).
- CorNewton3.m Computing the Nearest
Correlation Matrix with fixed diagonal and off diagonal elements (uploaded
on September 14, 2009).
- 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 semidefinite programming
with bound constraints. For details, check the following two papers:
[L.Q. Yang, D.F. Sun, and K.C. Toh, SDPNAL+: a majorized semismooth Newton-CG
augmented Lagrangian method for semidefinite
programming with nonnegative constraints, Mathematical Programming
Computation, 7 (2015), pp. 331-366.]
[X.Y. Zhao, D.F. Sun, and K.C. Toh, A Newton-CG
augmented Lagrangian method for semidefinite
programming, SIAM J. Optimization, 20 (2010), pp. 1737--1765.]
- SDPNAL-0.zip "A
Newton-CG augmented Lagrangian method for semidefinite programming" (first made
publicly available in September 2009 after a number of requests and trials
by many colleagues, for whom we would like to thank for their feedback and
suggestions). [This software solves large scale SDPs with linear
constraints plus several SDP cones and nonnegative orthants.
SOCs will be added in the next version. For each SDP block, the matrix
dimension n should not be much larger than 2000 though we did try n larger
than 4000. See here
for details.]
- Logdet-0.zip "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).
- PPApack-0.zip "Proximal-point
algorithms for nuclear norm minimizartion"
See here for
details.]
Codes
for rank constrainted 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
Recent
talks
Selected
Publications
Click here
for my google scholar page.
Technical
Reports
Unpublished
Technical Reports
- 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, PDF version Preference for
Travel Time.pdf; Revised in May 2013, PreferenceforTravelTime.pdf
- 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. PDF
version QP_dd_corrected.pdf.
2015-2016
·
Liang
Chen, Defeng Sun, and Kim Chuan
Toh, “An efficient inexact symmetric Gauss-Seidel
based majorized ADMM for high-dimensional convex
composite conic programming”, May 2015. Mathematical Programming XXX (2016) DOI 10.1007/s10107-016-1007-5. arXiv:1506.00741.
·
Defeng
Sun, Kim Chuan Toh, and
Liuqin Yang, “An efficient inexact ABCD method for least squares semidefinite programming”, May 2015, PDF version.pdf, SIAM Journal on Optimization 26 (2016) 1072--1100. Detailed
computational results for over 600 problems tested in the paper.
·
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 Lucien Polak on the occasion of his 85th birthday), February 2015, PDF version.pdf Journal of Optimization Theory and Applications XXX(2016) XXX-XXX.
·
Min
Li, Defeng Sun, and Kim Chuan
Toh, “A majorized ADMM with indefinite proximal
terms for linearly constrained convex composite optimization”, December 2014, PDF version.pdf, 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’’, November 2012,
PDF version.pdf Mathematical Programming XXX (2016) DOI
10.1007/s10107-015-0961-7.
·
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, PDF version SNDPPA-7.pdf 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, Final version Mathematical
Programming 155 (2016) 333-373.
·
Ying
Cui, Chenlei
Leng, and Defeng Sun, “Sparse
estimation of high-dimensional correlation matrices”, Computational Statistics & Data Analysis Vol. 93 (2016)
390–403.
·
Liuqin
Yang, Defeng Sun, and Kim Chuan
Toh, “SDPNAL+:
a majorized semismooth
Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints”, SDPNAL+ 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, Final PDF version
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”, AConvergent3-BlockADMM
SIAM Journal on Optimization Vol.
25, No. 2 (2015) 882–915. Detailed
computational results for over 400 problems tested in the paper.
Theses of Students:
- “Large Scale Composite Optimization Problems with
Coupled Objective Functions: Theory, Algorithms and Applications”, CuiYing_Thesis.pdf (PhD thesis of CUI Ying) January 2016.
- “An inexact Alternating Direction Method of Multipliers
for Convex Composite Conic Programming with Nonlinear Constraints", Thesis_DuMengyu.pdf (PhD thesis of
DU Mengyu) August 2015.
- “A Two-Phase Augmented Lagrangian
Method for Convex Composite Quadratic Programming", Thesis_LiXudong.pdf (PhD thesis of
LI Xudong) January 2015.
2013-2014
- 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.
- 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:
- ``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.
- "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.
2011-2012
- 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.
- 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.
Theses of Students:
2009-2010
- 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.
- 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:
- "Structured Low Rank Matrix Optimization Problems:
A Penalized Approach" PDF version main_gy.pdf (PhD
thesis of GAO Yan) August 2010.
- "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.
2007-2008
- 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.
- 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". Final PDF version final_SSZ_07.pdf Mathematical
Programming 114 (2008) 349--391. Published online: 10 May 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.
2005-2006
- 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," Final PDF version
Co_matrix_rev.pdf SIAM Journal on Matrix Analysis and Applications 28
(2006) 360--385. Code in Matlab
- 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.
- 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 Mathemtics 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
- 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. 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. 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 Mathematics, NUS.
Last Modified: February 5, 2016
Defeng Sun, Department of Mathematics, National University of Singapore