Sun, Defeng Professor Department of Mathematics

Brief History Research Interests Teaching Recruitments Professional Activities MATLAB Codes Recent 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 Gaomi County, Shandong Province, China; BSc and MSc from Nanjing University, China (1989, 1992) working on Variational Inequalities and Stochastic Optimization; PhD from Institute of Applied Mathematics, Chinese Academy of Sciences (1995) 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. I am also affiliated with the Risk Management Institute (RMI), NUS.

Recent Research Interests

• Matrix Programming: Basic Theory, Algorithms, and Applications
• Variational Analysis and Complementarity System
• Matrix Analysis and Computations
• Computational Finance: Financial Optimization
• Risk Management: Correlation stress test

Teaching

• MA5243 Advanced Mathematical Programming; Tuesday & Friday, 10:00am--12:00nn, S17, #05-12.

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 math dept, please visit their websites Karthik B. Natarajan , Kim Chuan TOH , and Gongyun ZHAO .
• Postdoctoral/Research Fellows: This year a couple of opennings are available, working with me and/or my colleague Kim Chuan TOH on modern optimization problems.

Professional Activities

• Associate Editor (December 2004) and editor-in-chief (October 2010 --), Asia-Pacific Journal of Operational Research.
• Associate Editor, Mathematical Programming, Series A (August 2007 --).
• Society Membership: INFORMS, Mathematical Programming Society, SIAM.

MATLAB Codes

Codes for nearest (covariance) correlation matrix problems

• CorNewton1.m Computing the Nearest Correlation Matrix (uploaded in August 2006; last modified September 10, 2009). [This code has been translated into C/C++ by many major banks and insurance companies. They are quite satisfied with the speed and accuracy. However, if you really need a faster code (for example, for a random 2000 by 2000 pseudo correlation matrix, the faster code needs less than 50 seconds in my PC for the calibration) than the one given here for large scale problems, please drop me an email.]
• 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 COnvex Matrix Optimization 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

• IQEP_Newton.m Computing the Inverse Quadratic Eigenvalue Problems Testing example: testIQEP_Newton.m (uploaded in March 2008).

Recent talks

• 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 revsied 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 Recent Publications

Technical Reports

• Chao Ding, Defeng Sun, and Kim Chuan Toh , "An introduction to a class of matrix cone programming", September 2010, PDF version IntroductionMCP_Sep_15.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.
• 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; See 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.

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) ???. 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, "An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem", PDF version CorrMatHnorm.pdf; IMA Journal of Numerical Analysis (2010). 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.
• "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).
• ``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.
• ``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'', 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.



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Last Modified: July 15, 2009
Defeng Sun, Department of Mathematics, National University of Singapore