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): Basic
Theory, Algorithms, and Applications
- Variational Analysis and Complementarity System
- Matrix Analysis and Computations
- Computational Finance: Financial Optimization
- Risk Management: Correlation stress test
Teaching
- 2014/2015, Semester I, ------
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
MATLAB
Codes
Codes
for nearest (covariance) correlation matrix problems
- CorrelationMatrixNewton.m
Computing the Nearest Correlation Matrix (uploaded in August 2006;
last updated on Janaury 22, 2014). This code should be good enough for
most users. However, if you really need a faster code, you need to
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 random 10,000 by 10,000 pseudo
correlation matrix, the faster 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
in my Dell Desktop with Intel (R) Core i7 processor. For practioners, you
may set the stopping criterion (relative duality gap) to stay between
1.0e-1 and 1.0e-3. . 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 implementation. (Updated on
January 25, 2014).
- 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-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
Recent Publications
Click here
for my google scholar page.
Technical
Reports
- 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.
- Weimin Miao, Shaohua Pan, and Defeng Sun, "A
rank-corrected procedure for matrix completion with fixed basis
coefficients", November 2012, PDF
version rank_correction.pdf.
- 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.
2013-2014
- 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 XX (2014/15) XXX—XXX.
- 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 PDF version Mathematical Programming XX (2014/15) XXX—XXX.
- Ying Cui, Chenlei
Leng, and Defeng Sun, "Sparse estimation of high-dimensional
correlation matrices”, PDF version Computational Statistics & Data
Analysis available online 13 October 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:
- "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. The software for solving convex
QSDPs with linear constraints plus several SDP cones, SOCs, and
nonnegative orthants will be made publicly available shortly after some
trials.]
- "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'', PDF version
Sun96.pdf Journal of Optimization Theory and Applications, Vol.
91, No.1, 1996, pp. 123--140.
- H. Jiang, L. Qi, X. Chen and D. Sun, ``Semismoothness
and Superlinear Convergence in Nonsmooth Optimization and Nonsmooth
Equations'', Nonlinear Optimization and Applications, G. Di Pillo
and F. Giannessi eds., (Plenum Publishing Corporation, New York), 1996,
197--212.
1995
- G. Liu, J. Han and D. Sun, ``Global convergence of BFGS
method with nonmonotone line search'', Optimization 34 (1995)
147--159.
- D. Sun, ``A new step-size skill for solving a class of
nonlinear projection equations'', PDF version
Sun95.pdf Journal of Computational Mathematics 13:4 (1995),
357--368.
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: August 6, 2014
Defeng Sun, Department of Mathematics, National University of Singapore