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 a small village (where
the story of Mo Yan’s award winning novel Red Sorghum took
place) located at Gaomi
County (高密县), 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
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 (first uploaded in August 2006; last
updated on May 11, 2017). 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 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, "CorrelationMatrix.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.]
- "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
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
old talks
Selected
Publications
Click here
for my google scholar page.
Technical
Reports
click
here for the arXived
- Shujun Bi, Shaohua Pan, and Defeng Sun, “A multi-stage convex relaxation
approach to noisy structured low-rank matrix recovery”, March
2017.
- Xudong
Li, Defeng Sun, and Kim Chuan Toh, “A highly efficient semismooth Newton augmented Lagrangian method for solving
Lasso problems’’, (an earlier shorter version https://arxiv.org/abs/1607.05428v1)
October 2016.
- 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.
2017--
·
Chao Ding, Defeng Sun, Jie Sun,
and Kim Chuan Toh, “Spectral operators of matrices”, Mathematical
Programming 16X (2017) XXX-XXX. [DOI: 10.1007/s10107-017-1162-3]. Revised
from the first part of https://arxiv.org/abs/1401.2269,
January 2014.
·
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 42 (2017) XXX—XXX. [Revised from the first part of arXiv:1508.02134,
August 2015.]
·
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 counterexample is designed to show that the
convergence analysis of ADMM in Boyd et al. (Found Trends Mach Learn
3(1):1–122, 2011) is incorrect with a correct proof supplied].
·
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. DOI 10.1007/s10107-016-1007-5.
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.
- 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.
Theses
of Students:
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:
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.
- 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.
Theses of Students:
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 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
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: July 22, 2017
Defeng Sun, Department of Mathematics, National University of Singapore