Welcome to Defeng Sun's Home Page

Defeng SUN (孙德锋) Professor Department of Mathematics National University of Singapore Republic of Singapore

Brief History Research Interests Teaching Recruitments Professional Activities MATLAB Codes Some old talks Publications

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

• 2017/2018, on leave.

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

• Associate Editor, Mathematical Programming (Series A, August 2007 --; Series B, January 2014--).
• 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 (July 2017--)
• Editor-in-chief Asia-Pacific Journal of Operational Research (October 2010 –December 2013). Advisory Committee Member from January 2014.
• 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: 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

• IQEP_Newton.m Computing the Inverse Quadratic Eigenvalue Problems Testing example: testIQEP_Newton.m (uploaded in March 2008; last updated on July 15, 2016 by Ying Cui (cuiying@u.nus.edu)).

Some old talks

• An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP (April 2012).
• From linear programming to matrix programming: A paradigm shift in optimization (December 2011).
• A sequential convex programming approach for rank constrained matrix optimization problems (December 2011).
• Low rank matrix optimization problems: Back to nonconvex regularizations (June 2011).
• Matrix optimization: Searching between the first and second order methods (May 2011).
• A majorized penalty approach for calibrating rank constrained correlation matrix problems (October 2010).
• An introduction to a class of matrix cone programming (July 2010).
• A majoried penalty approach for calibrating rank constrained correlation matrix problems (July 2010).
• Rank constrained matrix optimization problems (May 2010).
• An Introduction to Correlation Stress Testing (March 2010).
• An Implementable Proximal Point Algorithmic Framework for Nuclear Norm Minimization (July 2009).
• A Proximal Point Method for Matrix Least Squares Problem with Nuclear Norm Regularization (May 2009).
• A Newton-CG Augmented Lagrangian Method for Large Sacle Semidefinite Programming (based on a revised version) (March 2009).
• A Newton-CG Augmented Lagrangian Method for Large Sacle Semidefinite Programming (October 2008).
• Calibrating least squares covariance matrix problems with equality and inequality constraints (July 2008).
• The Role of Metric Projectors in Nonlinear Conic Optimization (August 2007).
• Inverse Quadratic Eigenvalue Problems (July 2006).
• Recent Developments in Nonlinear Optimization Theory (July 2006).
• A short summer school course on modern optimization theory: optimality conditions and perturbation analysis Part I Part II Part III (July 2006).

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:

• “The Metric Subregularity of KKT Solution Mappings of Composite Conic Programming”, (PhD thesis of GUO Han) March 2017.

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:

• “Large Scale Composite Optimization Problems with Coupled Objective Functions: Theory, Algorithms and Applications”, (PhD thesis of CUI Ying) January 2016.

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:

• “An inexact Alternating Direction Method of Multipliers for Convex Composite Conic Programming with Nonlinear Constraints”, (PhD thesis of DU Mengyu) August 2015.
• “A Two-Phase Augmented Lagrangian Method for Convex Composite Quadratic Programming”, (PhD thesis of LI Xudong) January 2015.

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:

• “Numerical Algorithms for a Class of Matrix Norm Approximation Problems”, PDF version Chen Caihua_Thesis_final.pdf (PhD thesis of former visiting student Caihua Chen from Nanjing University) June 2012.
• “An Introduction to A Class of Matrix Optimization Problems”, PDF version DingChao_Thesis_final.pdf (PhD thesis of DING Chao) January 2012.

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:

• “A penalty method for correlation matrix problems with prescribed constraints” (Master thesis of CHEN Xiaoquan) August 2011.

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.
• “A smoothing Newton-Bicgstab method for least squares matrix nuclear norm problems” (Master thesis of LUO Yanying) January 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.
• 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:

• “An inexact SQP Newton method for convex SC1 minimization problems” (Master thesis of CHEN Yidi)

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

• 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”, 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.

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:

• “Smoothing Approximations for Two Classes of Convex Eigenvalue Optimization Problems” PDF version Yu_Aug_2005.pdf (Master thesis of YU Qi)
• “A Smoothing Newton Method for the Boundary-Valued ODEs” PDF version Zheng_May_2005.pdf (Master thesis of ZHENG Zheng)

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:

• “Smooth Convex Approximation and Its Applications” PDF version Shi_July_2004.pdf (Master thesis of Shengyuan SHI)
• “The Smoothing Function of the Nonsmooth Matrix Valued Function” PDF version Zhao_July_2004.pdf (Master thesis of Jinye ZHAO)

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

• 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'', Journal of Computational Mathematics 13:4 (1995), 357--368.

• D. F. Sun, Algorithms and Convergence Analysis for Nonsmooth Optimization and Nonsmooth Equations, PhD thesis (submitted in December 1994 and defended in March 1995), Institute of Applied Mathematics, Chinese Academy of Sciences.

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.

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Last Modified: July 22, 2017
Defeng Sun, Department of Mathematics, National University of Singapore