SUN Defeng Department of Mathematics National University of Singapore

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

Office:

S14, #04-25

Phone:

+65 6516 3343

Fax:

+65 6779 5452

Email:

matsundf@nus.edu.sg

Mail:

Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore 117543, Republic of Singapore

Brief History

Born in Gaomi County, Shandong Province, China; BSc and MSc from Nanjing University, China (1989, 1992) with focus in Variational Inequalities and Stochastic Optimization; PhD from Institute of Applied Mathematics, Chinese Academy of Sciences (1995) under the supervision of Professor Jiye Han with focus in 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 Optimization; I have been with Department of Mathematics, National University of Singapore since December 2000.

Recent Research Interests

• Semidefinite Optimization: Basic Theory, Algorithms, and Applications
• Variational Analysis
• Complementarity System
• Matrix Analysis and Computations
• Computational Finance; Financial Optimization; Risk Management

Teaching

• No teaching duty this semester. On sabbatical leave from August 18, 2008 to June 17, 2009
• For weekly optimization seminar, please contact Dr Yongjin Liu at smaly@nus.edu.sg. The time is: Wednesday, 9:00--11:00am.

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 Karthik B. Natarajan , Kim Chuan TOH , and Gongyun ZHAO ,
• Postdoctoral/Research Fellows: Each year, a couple of opennings are available, working with me and/or my colleague Kim Chuan TOH on modern optimization problems. Drop me an email to check the availability before submit your application.

Professional Activities

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

MATLAB Codes

• CorNewton.m Computing the Nearest Correlation Matrix (August 2006; last modified March 2008). [If you really need a 5-10 times faster code than the one given here for large scale problems, please drop me an email.]
• CorNewton1.m Computing the Nearest Positive Correlation Matrix (December 2006; last modified March 2008).
• CorMatWnorm.m Computing the W-norm Nearest Correlation Matrix Testing example: testCorMatWnorm.m (uploaded in June 2008).
• CorMatHdm.m Computing the H-weightd Nearest Correlation Matrix . Testing example: testCorMatHdm.m (uploaded in June 2008).
• LagDualNewton.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 Testing example: testAugLagNewton.m (AugLagNewton method for the Band Correlation Stress Testing, "CorNewton1.m" will be called) (March 2007)
• IQEP_Newton.m Computing the Inverse Quadratic Eigenvalue Problems Testing example: testIQEP_Newton.m (uploaded in March 2008).
• CaliMat.m Calibrating Covariance Matrix Problems with Inequality Constraints Testing example: test_CaliMat.m (uploaded in June 2008).

Recent talks

• 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

• Yan Gao and Defeng Sun, "Calibrating least squares covariance matrix problems with equality and inequality constraints", June 2008. PDF version CaliMat_June_2008.pdf 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", March 2008. PDF version aug_new_03_2008.pdf
• Houduo Qi and Defeng Sun, "An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem", March 2008. PDF version Cor_matrix_H_Mar_08.pdf 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", March 2007. PDF version stress_test_March20_07.pdf See the "MATLAB Codes" section for codes in Matlab.

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) ??. Published online: June 19, 2008.
• 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.
• F. Meng, D.F. Sun and G. 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: August 14, 2008
Defeng Sun, Department of Mathematics, National University of Singapore