Xiaojun Chen

Research Interests

• Iterative methods for nonlinear/singular/nonsmooth equations
• Complementarity problems and applications
• Nondifferentiable optimization
• Verification methods
• Stochastic optimization and parallel computation
• Spherical t-Designs

Recent Research Grants:

• Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Solutions of Parametric Linear Complementarity Problems ", 2009-2011.
• Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Robust Algorithms for Singular Smooth and Nonsmooth Equations ", 2008-2010.
• Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Large-scale Constrained Nonlinear Least Squares Problems and Applications in Engineering and Economics ", 2008-2010.
• Fund for Promotion of International Scientific Research (B1) (2007)
• Hirosaki University President Key Research Project:
  Optimization methods for asset management concerning risk and natural disasters (2004-2005)
• Scientific research grant-in-aid (C) from JSPS(Japan Society for the Promotion of Science):
  Robust numerical methods for nonlinear equations (2004-2006)
• Scientific research grant-in-aid (C) from JSPS:
  Numerical methods for nonsmooth equations (2002-2003)
• Scientific research grant-in-aid (C) from the Ministry of Education, Science, Sport and Culture of Japan :
  Smoothing Newton methods for nondifferentiable equations (1999-2000)
• ARC (Australian Research Council) large grant:
  Smoothing and non-interior point methods (with L.Qi and M.Fukushima) (1999-2001)
• ARC Small grant:
  Iterative solution of nondifferentiable saddle point problems (1998)
• ARC research fellow grant:
  Nonsmooth equations and parallel algorithms (1995-1998)

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  Activities:

  • Invited Speaker:
    The International Conference on Continuous Optimization(ICCOPT), Santiago, Chile,
    July 26-29, 2010
    
  • Member of Committee of Mathematical Society of Japan(2004-2005)
  • Reviewer of Mathematical Reviews.
  • Memberships:
    Mathematical Society of Japan (1999-2008)
    Japan Society for Industrial and Applied Mathematics (1999-2008)
    The operations Research Society of Japan (2000-2008)
    
  • The Pacific Optimization Research Activity Group

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  • Adjunct Professor of Xi'an Jiaotong University (11.2004--)
  • Adjunct Professor of Graduate University of the Chinese Academy of Sciences (3.2005--)

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  Editor:

  • Computing, Springer Wien, New York
  • Numerical Functional Analysis and Optimization, Taylor & Francis, New York.
  • Numerical Algorithms, Kluwer Academic Publishers, The Netherlands.
  • Journal of Industrial and Management Optimization, The American Institute of Mathematical Sciences, Springfield, USA.

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  Teaching

  • Compuational Mathematics
  • Numerical Analysis
  • Optimization
  • Calculus
  • Differential Equations
  • Managerial Decision Science
  • Engineering Optimization

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  Special Issues for Journals

  • X. Chen, M.Z. Nashed and T. Yamamoto, eds, Numerical Methods and Verification of Solutions, Numerical Functional Analysis and Optimization, Marcel Dekker, Inc. New York, June 2001.
    
  • G. Alefeld and X. Chen, eds, Topics in Numerical Analysis with Special Emphasis on Nonlinear Problems, Computing, Springer-Verlag Wien, Austria, September 2001.
  • G. Alefeld, X. Chen and T. Yamamoto, Recent Advances in Computational Mathematics, Journal of Computational and Applied Mathematics, Elsevier Science Publishers, North-Holland, 2003.

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    Text Book

  • X. Chen and T. Yamamoto, Numerical Analysis for Science and Engineering, Corona Publisher, 2002. (3rd Reprints, 2008)

  Research Papers

  • X. Chen and S. Xiang, Implicit solution function of P0 and Z matrix linear complementarity constraints, to appear in Math. Programming.
  • C. Zhang and X. Chen, Smoothing projected gradient method and its application to stochastic linear complementarity problems, SIAM J. Optimization 20(2009) 627-649.
  • X. Chen and J. Ye, A class of quadratic programs with linear complementarity constraints, to appear in Set-Valed and Variational Analysis.
  • T, Kimura and X. Chen, Validated solution of saddle point linear systems, SIAM J. Matrix Anal. Applications 30(2009) 1697-1708.
  • Y Shi, Y. Tian, X. Chen, and P. Zhang, Regularization mulitiple criteria linear programs for classification, to appear in Science in China Series F: Information Sciences.
  • X. Chen and S. Mahmoud, Implicit Runge-Kutta methods for Lipschitz continuous ordinary differential equations , SIAM J. Numer. Anal. 46(2008) 1266-1280
  • X. Chen and S. Xiang, Perturbation bounds of P-matrix linear complementarity problems , SIAM J. Optimization 18(2007) 1250-1265.
  • C. Zhang, X. Chen and N. Xiu, Global error bounds for the extended vertical LCP, Computational Optimization and Applications 42(2009) 335-352
  • G. Alefeld and X. Chen, A regularized projection method for complementarity problems with non-Lipschitzian functions, Mathematics of Computation 77(2008) 379-395
  • C. Zhang and X. Chen, Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty, Journal of Optimization Theory and Applications 137(2008) 277-295
  • G. Lin, X. Chen and M. Fukushima, New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC, Optimization 56(2007) 641-653.
  • G. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming 116(2009) 343-368
  • H. Fang, X. Chen and M. Fukushima, Stochastic R0 matrix linear complementarity problems , SIAM J. Optimization 18(2007) 482-506.
  • X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems , Mathematical Programming 117(2009) 51-80
  • X. Chen and R. Womersley, Existence of solutions to systems of underdetermined equations and spherical designs , SIAM J. Numerical Analysis 44(2006) 2326-2341 Talk
  • X. Chen and T. Kimura, Finite element surface fitting for bridge management, International J. Information Technology & Decision Making (2006) 671-681
  • X. Chen and S. Xiang, Computation of error bounds for P-matrix linear complementarity problem , Mathematical Programming 106(2006) 513-525.
  • X. Chen and M. Fukushima, Expected Residual Minimization Method for Stochastic Linear Complementarity Problems, Mathematics of Operations Research 30(2005) 1022-1038.
  • X. Chen, Finite Difference Smoothing Solution of Nonsmooth Constrained Optimal Control Problems , Numerical Functional Analysis and Optimization 26(2005) 49-68
  • C. Ling, X. Chen, M. Fukushima and L. Qi, A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems, Pacific Journal of Optimization 1 (2005) 127-145.
  • X. Chen, First order conditions for nonsmooth discretized constrained optimal control problems, SIAM J Control and Optimazation, 42(2004) 2004-2015.
  • G. Kou, Y. Peng, Y. Shi, Z. Chen, X. Chen, A multiple-criteria quadratic programming approach to network intrusion detection. Lecture Notes in Computer Science 3327, Yong Shi, Weixuan Xu, Zhengxin Chen,eds., (Springer-Verlag GmbH, 2004) 145-153
  • X. Chen and K. Hashimoto, Numerical validation of solutions of saddle point matrix equations, Numerical Linear Algebra with Applications, 10(2003) 661-672.
  • X. Chen and M. Fukushima, A smoothing method for a mathematical program with P-matrix linear complementarity constraints, Computational Optimization and Applications, 27(2004) 223-246.
  • X. Chen and K. Hashimoto Verication methods for nonlinear equations with saddle point functions, Journal of Computational and Applied Mathematics, 159(2003),13-24.
  • Z. Wei, L. Qi and X. Chen, An SQP-type method and its application in stochastic programs, Journal of Optimization Theory and Applications, 116(2003),205-228.
  • B. Mermri and X. Chen, On characterizations and regularity of the solution of bilateral obstacle problems, Journal of Computational and Applied Mathematics, 152(2003), 333-345.
  • X. Chen, Applications of smoothing methods in numerical analysis and optimization, Journal of Asian Information Science Life, 1(2002), 1-13.
    
  • G.E. Alefeld, X. Chen, F.A.Potra, Numerical validation of solutions of complementarity problems: the nonlinear case, Numerische Mathematik, 92(2002) 1-16.
    
  • X. Chen, L. Qi and Y. Yang, Lagrangian globalization methods for nonlinear complementarity problems, Journal of Optimization Theory and Applications, 112(2002) 77-95.
    
  • X. Chen, On convergence of SOR methods for nonsmooth equations, Numerical Linear Algebra with Applications, 9(2002)81-92.
    
  • T. Yamamoto, Q. Fang and X. Chen, Superconvergence and nonsuperconvergence of the Shortley-Weller approximations for Dirichlet problems, Numerical Functional Analysis and Optimization, 22(2001) 455-470.
    
  • X. Chen, A superlinearly and globally convergent method for reaction and diffusion problems with a non-Lipschitzian operator, Computing[Suppl], 15(2001) 79-90.
    
  • X. Chen, Y. Shogenji and M. Yamasaki, Verification for existence of solutions of linear complementarity problems, Linear Algebra and Its Applications, 324 (2001) 15-26.
    
  • X. Chen and Y. Ye, On smoothing methods for the P_0 matrix linear complementarity problem, SIAM J. Optimization. 11(2000) 341-363.
    
  • X. Chen, Z. Nashed and L. Qi, Smoothing methods and semismooth methods for nondifferentiable operator equations SIAM J. Numerical Analysis. 38 (2000) 1200-1216.
    
  • X. Chen, Newton-type methods for stochastic programming, Mathematical and Computer Modelling. 31 (2000) 89-98.
    
  • B. Chen, X. Chen and C. Kanzow, A penalized Fischer-Burmeister NCP-function, Mathematical Programming. 88 (2000) 211-216.
    
  • X. Chen, Smoothing methods for complementarity problems and their applications: a survey, Journal of the Operations Research Society of Japan, 43(2000) 32-47.
    
  • B. Chen and X. Chen, A global linear and local quadratic continuation smoothing method for variational inequalities with box constraints, Computational Optimization and Applications. 17(2000) 131-158.
  • X. Chen and R. Womersley, Random test problems and parallel methods for quadratic programs and quadratic stochastic programs, Optimization Methods and Softwares. 13(2000) 275-306.
    
  • G.E. Alefeld, X. Chen and F.A. Potra, Numerical validation of solutions of linear complementarity problems Numerische Mathematik, 83 (1999) 1-23 .
    
  • B. Chen and X. Chen, ``A Global and Local Superlinear Continuation-Smoothing Method for P_0 and R_0 NCP or Monotone NCP'', SIAM J. Optimization, 9 (1999) 624-645.
    
  • X. Chen and Y. Ye, ``On homotopy-smoothing methods for variational inequalities'', SIAM J. Control and Optimization, 37 (1999) 587-616.
    
  • X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Math. Programming, 85(1999) 313-334.
    
  • X. Chen, ``On preconditioned Uzawa Methods and SOR methods for saddle point problems'' J. Comp. Appl. Math. 100(1998) 207-224.
    
  • X. Chen, ``Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings'', SIAM J. Numerical Analysis, 35(1998) 1130-1148.
    
  • X.Chen, N. Matsunaga and T. Yamamoto, ``Smoothing Newton methods for nonsmooth Dirichlet problems'', Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods M. Fukushima and L. Qi, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1998) 65-79.
    
  • X. Chen, ``A verification method for solutions of nonsmooth equations'', Computing, 58(1997) 281-294. .
    
  • 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'', Mathematics of Computation, 67(1998), 519-540.
    
  • X. Chen, ``Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations'', J. Comp. & Appl. Math. 80(1997),105-126.
    
  • L. Qi and X. Chen, ``A preconditioning proximal Newton method for nondifferentiable convex optimization'', Math. Programming, 79(1997) 411-429.
    
  • X. Chen, M.Z. Nashed and L. Qi, ``Convergence of Newton's method for singular smooth and nonsmooth equations using adaptive outer inverses'', SIAM J. Optim. 7 (1997) 445-462.
    
  • X. Chen, ``A parallel BFGS-SQP method for stochastic linear programs'', Computational Techniques and Applications 1995, Eds by A. Easton and R. May, World Scientific, (1996) pp. 177-184.
    
  • X. Chen, ``Convergence of the BFGS method for LC1 constrained optimization'', SIAM J. Control and Optim., 34(1996) 2051-2063
    
  • X. Chen and R.S. Womersley, ``A parallel inexact Newton method for stochastic programs with recourse'', Annals of Operations Research, 64(1996), 113-141.
    
  • 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 Press, New York, 1996) 197-212.
    
  • X. Chen, L. Qi and R.S. Womersley, ``Newton's method for quadratic stochastic programs with recourse'', J. Comp. & Appl. Math., 60 (1995), 29-46.
    
  • L. Qi and X. Chen, ``A globally convergent successive approximation method for severely nonsmooth equations'', SIAM J. Control and Optimization, 33 (1995), 402-418.
    
  • X. Chen and L. Qi, ``A parameterized Newton method and a quasi-Newton method for solving nonsmooth equations'', Comp. Optim. Appl., 3(1994), 157-179.
    
  • X. Chen and T. Yamamoto, ``Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable term'', J. Comp. Appl. Math., 55(1994), 311-324.
    
  • M.Z. Nashed and X. Chen, ``Convergence of Newton-like methods for singular operator equations using outer inverses'', Numer. Math., 66(1993), 235-257.
    
  • X. Chen and T. Yamamoto, A convergence ball for multistep simplified Newton-like methods, Numerical Functional Analysis and Optimization, 14(1993), 15-24.
    
  • X. Chen and T. Yamamoto, On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators, Computing, 49(1992), 87-94.
    
  • X. Chen and T. Yamamoto, PCG methods applied to a system of nonlinear equations, Journal Computational and Applied Mathematics, 38(1991), 61-75.
    
  • X. Chen, On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms, Annals of the Institute of Statistical Mathematics, 42(1990), 387-401.
    
  • T. Yamamoto and X. Chen, An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations, Journal Computational and Applied Mathematics, 30(1990), 87-97.
    
  • T. Yamamoto and X. Chen, Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equations, Japan Journal Applied Mathematics, 7(1990), 131-143.
    
  • T. Yamamoto and X. Chen, Validated methods for solving nonlinear systems, Information Processing, 31(1990), 1191-1196.
    
  • X. Chen and D. Wang, On the optimal properties of the Krawczyk-type interval operator, International Journal of Computer Mathematics, 29(1989), 235-245.
    
  • X. Chen and T. Yamamoto, Convergence domains of certain iterative methods for solving nonlinear equations, Numerical Functional Analysis and Optimization, 10(1989), 37-48.
    
  • X. Chen and T. Yamamoto, A necessary and sufficient condition for convergence of certain iterative methods for nonlinear equations, in International Series of Numerical Mathematics, Vol.86(Edited by R.P. Agarwal and others), 95-104, Birkh\"{a}user Verlag, Basel 1988.
    
  • Z. You and X. Chen, Interval iterative methods for nonlinear numerical equations under partial ordering (II), Journal of Computational Mathematics, 6(1988), 318-324.
    
  • Z. You and X. Chen, Interval iterative methods for nonlinear numerical equations under partial ordering(I), Journal of Computational Mathematics, 6(1988), 39-47.
    
  • Z. You and X. Chen, A two-sided interval iterative method for the finite dimensional nonlinear system, Journal of Computational Mathematics, 5(1987), 307-315.
    
  • Z. You and X. Chen, A continuation-interval method for nonlinear systems, Science Bulletin, 33(1987), 270-273.
    
  • Z. You and X. Chen, A two-sided interval iterative method suitable for arbitrary initial conditions, Communications on Applied Mathematics and Computing, 1(1987), 58-64.
    
  • Z. You and X. Chen, On two-sided interval relaxation methods, Science Bulletin, 31(1986), 1521-1524.
    
  • Z. You and X. Chen, A two-sided interval iterative method of Seidel type for nonlinear systems, Numerical Mathematics, A Journal of Chinese Universities, 8(1986), 274-282.
    
  • X. Chen and D. Wang, A parallel conjugate direction method for unconstrained optimization problems, Numerical Mathematics, A Journal of Chineses Universities, 8(1986), 120-127.
    
  • D. Wang and X. Chen, Interval relaxation methods for nonlinear systems of nonlinear equations, Mathematics Numerical Sinica, 7(1985), 426-432.
    
  • Z. You and X. Chen, The conjugate direction method with pattern searches in subspace, Numerical Mathematics, A Journal of Chineses Universities, 7(1985), 300-307.
    
  • Z. You and X. Chen, A decomposition coordination algorithm for a large-scale programming, Mathematics Numerical Sinica, 7(1985), 247-252.
    
  • D. Wang and X. Chen, A decomposition and parallel algorithm for a sort of large-scale minimization problems, Journal of Engineering Mathematics, 1(1984), 129-136.
    
  • X. Chen, Decomposition parallel algorithms for a kind of special minimum problem, Journal of Chengdu University of Science and Technology, (1984), 115-122.
    
  • X. Chen, Improvement of the D.S.C. and Rosenbrock methods, Journal Chengdu University of Science and Technology, (1983), 45-52.
    
  • X. Chen, An improved D.S.C. algorithm, Science Bulletin, 20(1983), 1276.
    
  • R. Zhao, X. Chen, Turn-jump direct search method, Journal Xi'an Jiaotong University, 17(1983), 93-100.
    
  • R. Zhao, X. Chen, The universal definition of neartude for the fuzzy subsets and the grade of imprecision, Journal Xi'an Jiaotong University, 15(1981)

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    Reports and Fortran 90 Code

    
    
    • Xiaojun Chen, Andreas Frommer and Bruno Lang, Computational Existence Proofs for Spherical t-Designs
    • Chao Zhang, Xiaojun Chen and Agachai Sumalee, Wardrop's User Equilibrium Assignment under Stochastic Environment
    • X.Chen, Fengmin Xu and Yinyu Ye, Lower bound theory of nonzero entries in solutions of l_2-l_1 minimization
    • X. Chen and S. Xiang, Examples of Perturbation bounds of P-matrix linear complementarity problems
      
    • X. Chen and R. Womersley, Random test problems and parallel methods for quadratic programs and quadratic stochastic programs, Optimization Methods and Softwares. Fortran 90 code for generating multiple quadratic programs
      
    • J. Birge, X. Chen and L. Qi, A stochastic Newton method for stochastic quadratic programs with recourse, Applied Mathematics Report AMR 94/9, School of Mathematics, University of New South Wales.

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  Hirosaki University

  UNSW