Chen Xiaojun

Chair Professor of Applied Mathematics

Head of Department of Applied Mathematics(2013.7--2019.6)

Associate Director of University Research Facility in Big Data Analytics(2017.7--2020.6)

Director of University Research Facility in Big Data Analytics(2020.7--)

Co-Director of CAS AMSS-PolyU Joint Laboratory of Applied Mathematics(2019.1--)

SIAM fellow


Office:

Room TU728, Yip Kit Chuen Building

Phone:

+852 2766 6925

Fax:

+852 2362 9045

Email: maxjchen [at] polyu.edu.hk

Mail:

Department of Applied Mathematics

The Hong Kong Polytechnic University

Hung Hom, Kowloon, Hong Kong, China


Research Interests

  • Stochastic Equilibrium Problems

  • Iterative methods for nonlinear/singular/nonsmooth equations

  • Complementarity problems and applications

  • Nonsmooth, nonconvex optimization

  • Verification methods

  • Spherical t-Designs

  • Requirements PhD Students: Hold a postgraduate degree in Mathematics and satisfy English requirement (e.g. IELTS 6.5, or TOEFL 80), Hong Kong PhD Fellowship Scheme


Recent Research Grants:

  • Principal Investigator: RGC Grant "Nonsmooth nonconvex finite-sum optimization for deep neural networks'', 2020-2022.

  • Principal Investigator: RGC Grant "Nonsmooth optimization problems with group sparsity penalties", 2019-2021.

  • Principal Investigator: RGC Grant "Optimization Theory and Algorithms for Two-stage Stochastic Variational Inequalities", 2018-2020.

  • Principal Investigator: RGC Grant "Efficient Regularization Methods for Partially Separable Nonsmooth Nonconvex Optimization ", 2017-2019.

  • Principal Investigator: RGC Grant "Analysis and computation of sparse solutions of linear complementarity problems with applications", 2016-2018.

  • Principal Investigator: RGC Grant, "Penalty methods for nonconvex nonsmooth constrained minimization", 2015-2017.

  • Principal Investigator: NSFC/RGC Joint Research Schems, "Sparse Optimization: Algorithms and Theories", 2014-2018.

  • Principal Investigator: RGC Grant, "Smoothing regularization methods for parametric variational inequality problems", 2014-2016.

  • Principal Investigator: RGC Grant, "Second-Order Numerical Methods for Nonsmooth Optimization", 2013-2015.

  • Principal Investigator: RGC Grant, "Regularized Minimization Problems in High Dimensions", 2012-2014.

  • Principal Investigator: RGC Grant, "Optimization Reformulations and Algorithms for Variational Inequalities under Uncertainty", 2011-2013.

  • Principal Investigator: RGC Grant, "Efficient Methods for Nonsmooth, Nonconvex Optimization", 2010-2012.

  • Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Robust Algorithms for Nonsmooth Nonconvex Optimization with Applications", 2010-2012.

  • Principal Investigator: RGC Grant, "Solutions of Parametric Linear Complementarity Problems", 2009-2011.

  • Principal Investigator: RGC 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)


Conferences:




Activities:

  • Adjunct Professor of Xi'an Jiaotong University (11.2004--)

  • Adjunct Professor of Graduate University of the Chinese Academy of Sciences (3.2005--)


Editor:

Area Editor


Special Issues for Journals

  • X. Chen and R. Wets, eds, Stochastic Equilibrium and Variational Inequalities in Mathematical Programming B, 2017.

  • X. Chen and N. Yamashita, eds, Optimization and Equilibrium problems, Computational Optimization and Applications, Springer-Verlag Wien, Austria, 2014.

  • X. Chen and M. Fukushima, eds, Applied and Computational Optimization, Computational Optimization and Applications, Springer-Verlag Wien, Austria, 2011.

  • O. Axelsson and X. Chen, eds, Matrix Computations and Nonlinear Equations, Numerical Linear Algebra with Applications, Elsevier Science Publishers, North-Holland, 2011.

  • C.K. Chan, X. Chen, L. Qi, C. Rogers, Z.C. Shi and I.H. Sloan, eds, Engineering and Computational Mathematics, Journal of Computational and Applied Mathematics, Elsevier Science Publishers, North-Holland, 2011.

  • X. Chen, Z. Chen and G. Lin, eds, Stochastic Optimization, Pacific Journal of Optimization, Yokohama Publishers, Tokyo, 2011.

  • 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.


Text Book

  • X. Chen and T. Yamamoto, Numerical Analysis for Science and Engineering, Corona Publisher, 2002. (4th Reprints, 2017)


Research Papers

  1. C. Li and X. Chen, Isotropic non-Lipschitz regularization for sparse representations of random fields on the sphere, to appear in Math. Comp.

  2. F. He, X. Wang, and X. Chen, A penalty relaxation method for image processing using Euler's elastica model, SIAM J. Imaging Sciences, 14(2021), 389-417.

  3. W. Bian, X. Chen and C.T. Kelley, Anderson acceleration for a class of nonsmooth fixed-point problems, to appear in SIAM J. Scientific Computing.

  4. L. Pan and X. Chen, Group Sparse Optimization for Images Recovery Using Capped Folded Concave Functions, SIAM J. Imaging Sciences, 14 (2021), 1-25.

  5. X. Chen and Ph.L. Toint, High-Order Evaluation Complexity for Convexly-Constrained Optimization with Non-Lipschitzian Group Sparsity Terms, to appear in Math. Programming.

  6. L. Guo and X. Chen, Mathematical Programs with Complementarity Constraints and a Non-Lipschitz Objective: Optimality and Approximation, Math. Programming, 185(2021), 455-485.

  7. S. Wu, T. Zhou and X. Chen, A Gauss-Seidel type method for dynamic nonlinear complementarity problems, SIAM J. Control and Optimization, 58(2020), 3389-3412.

  8. W. Bian and X. Chen, A smoothing proximal gradient algorithm for nonsmooth convex regression with cardinality penalty, SIAM J. Numerical Analysis, 58(2020), 858-883.

  9. J. V. Burke, X. Chen and H. Sun, The Subdifferential of Measurable Composite Max Integrands and Smoothing Approximation, Math. Programming, 181(2020),229-264.

  10. C. Zhang and X. Chen, A Smoothing Active Set Method for Linearly Constrained Non-Lipschitz Nonconvex Optimization, SIAM Optimization, 30(2020), 1-30.

  11. T. Liu, Z. Lu, X. Chen and Y.-H. Dai, An exact penalty method for semidefinite-box constrained low-rank matrix optimization problems, IMA J. Numerical Analysis, 40(2020), 563-586.

  12. X. Chen, H. Sun and H. Xu, Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems, Math. Programming, 177 (2019), 255-289.

  13. X. Chen, Ph. L. Toint and H. Wang, Complexity of partially-separable convexly-constrained optimization with non-Lipschitzian singularities, SIAM J. Optimization, 29(2019), 874-903.

  14. X. Chen and T. Kelley, Convergence of the EDIIS Algorithm for Nonlinear Equations, SIAM J. Scientific Computing, 41(2019), A365-379.

  15. X. Chen, A. Shapiro and H. Sun, Convergence analysis of sample average approximation of two-stage stochastic generalized equations, , SIAM J. Optimization, 29(2019), 135-161.

  16. L. Yang, T.K. Pong and X. Chen, A non-monotone alternating updating method for a class of matrix factorization problems, SIAM J. Optimization, 28(2018), 3402-3430.

  17. X. Chen and R. Womersley, Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere, SIAM J. Imaging Sciences. 11(2018), 1390-1415.

  18. X. Chen, T. Kelley, F. Xu and Z. Zhang, A smoothing direct search method for Monte Carlo-based constrained nonsmooth nonconvex optimization, SIAM J. Scientific Computing. 40(2018), A2174-A2199.

  19. B. Gao, X. Liu, X. Chen and Y. Yuan, A new first-order algorithmic framework for optimization problems with orthogonality constraints, SIAM J. Optimization, 28(2018) 302-332.

  20. Z. Wang and X. Chen, An exponential integrator based discontinuous Galerkin method for linear complementarity systems, IMA J. Numerical Analysis, 38(2018), 2145-2165.

  21. Y. Zhou amd X. Chen, Spherical t_\epsilon-designs for approximations on the sphere, Mathematics of Computation, 87(2018), 2831-2855.

  22. Z. Lu and X. Chen, Generalized conjugate gradient methods for L_1 regularized convex quadratic programming with finite convergence, Mathematics of Operations Research, 43(2018), 275-303.

  23. S. Wu and X. Chen , A parallel iterative algorithm for differential linear complementarity problems, SIAM J. Scientific Computing, 39(2017), A3040-A3066.

  24. W. Bian and X. Chen, Optimality and complexity for constrained optimization problems with nonconvex regularization, Mathematics of Operations Research, 42(2017), 1063-1084.

  25. X. Chen, T.K. Pong and R. Wets, Two-stage stochastic variational inequalities: an ERM-solution procedure, Math. Programming, 165(2017), 71-112.

  26. Hailin Sun, Che-Lin Su and Xiaojun Chen, SAA regularized methods for multi-product price optimization under the pure characteristics demand model, Math. Programming, 165(2017), 361-390.

  27. X. Chen, L. Guo, Z. Lu and J.J. Ye, An augmented Lagrangian method for non-Lipschitz nonconvex programming, SIAM J. Numerical Analysis, 55(2017), 168–193.

  28. B. Wen, X. Chen and T.K. Pong, Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconve nonsmooth minimization problems, SIAM J. Optimization, 27(2017), 124–145.

  29. L. Yang, T.K. Pong and X. Chen, Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction, SIAM J. Imaging Sciences, 10(2017), 74–110.

  30. X. Chen, Z. Lu and T.K. Pong, Penalty methods for a class of non-Lipschitz optimization problems, SIAM J. Optimization, 26 (2016), 1465-1492.

  31. X. Chen and S. Xiang, Sparse solution of linear complementarity problems, Math. Programming, 159 (2016), 539-556.

  32. W. Bian and X. Chen, Linearly constrained non-Lipschitz optimization for image restoration, SIAM J. Imaging Sciences. 8(2015), 2294-2322.

  33. J. Willert, X. Chen, and C. T. Kelley, Newton's method for Monte Carlo-based residuals, SIAM J. Numer. Anal., 53(2015), 1738-1757.

  34. X. Chen, H. Sun and R. Wets, Regularized mathematical programs with stochastic equilibrium constraints: estimating structural demand models, SIAM J. Optim., 25(2015), 53-75.

  35. W. Bian, X. Chen and Y. Ye, Complexity analysis of interior point algorithms for non-Lipschitz and nonconvex minimization, Math. Programming, 149(2015), 301-327.

  36. X. Chen and Z. Wang, Differential variational inequality approaches to dynamic games with shared constraints, Math. Programming, 146(2014), 379-408.

  37. X. Chen, D. Ge, Z. Wang and Y. Ye, Complexity of Unconstrained L2-Lp Minimization, Math. Programming, 143 (2014), 371-383.

  38. W. Bian and X. Chen, Neural network for nonsmooth, nonconvex constrained minimization via smooth approximation, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 545-556.

  39. X. Chen and W. Zhou, Convergence of the reweighted l_1 minimization algorithm for l_2-l_p minimization, Comp. Optim. Appl. 59(2014), 47-61.

  40. W. Bian and X. Chen, Worst-case Complexity of Smoothing Quadratic Regularization Methods for non-Lipschitzian Optimization, SIAM J. Optim. 23 (2013), 1718-1741. Matlab Code

  41. X. Chen and Z. Wang, Convergence of regularized time-stepping methods for differential variational inequalities, SIAM J. Optim. 23 (2013), 1647-1671.

  42. X. Chen, L. Niu and Y. Yuan, Optimality conditions and smoothing trust region Newton method for non-Lipschitz optimization, SIAM J. Optim. 23 (2013), 1528-1552.

  43. X. Chen and S. Xiang, Newton iterations in implicit time-stepping scheme for differential linear complementarity systems, Mathematical Programming, 138(2013), 579-606.

  44. X. Chen and Z. Wang, Computational Error Bounds for Differential Linear Variational Inequality, IMA Journal of Numerical Analysis, 32(2012), 957-982.

  45. X. Chen, M. Ng and C. Zhang, Nonconvex l_p regularization and box constrained model for image restoration, IEEE Trans. Image Processing, 21(2012), 4709-4721

  46. X. Chen, Smoothing Methods for Nonsmooth, Novonvex Minimization, Mathematical Programming.134(2012), 71-99.

  47. X. Chen, R. B-J Wets and Y. Zhang, Stochastic Variational Inequalities: Residual Minimization Smoothing/Sample Average approximations, SIAM J. Optimization, 22(2012), 649-673.

  48. C. An, X. Chen, I.H. Sloan, R. S. Womersley, Regularized least squares approximations on the sphere using spherical designs ,SIAM J. Numerical Analysis, 50(2012), 1513-1534.

  49. W. Bian and X. Chen, Smoothing Neural Network for Constrained Non-Lipschitz Optimization with Applications, IEEE Trans. Neural Networks, 23(2012) 399-411.

  50. X. Chen, R. Womersley and J. Ye, Minimizing the Condition Number of a Gram Matrix, SIAM J. Optimization, 21(2011), 127-148. Talk, Photo

  51. C. Zhang, X. Chen and A. Sumalee, Robust Wardrop’s User Equilibrium Assignment under Stochastic Demand and Supply: Expected Residual Minimization Approach, Transportation Research Part B 45(2011), 534-552.

  52. X. Chen and S. Xiang, Implicit solution function of P0 and Z matrix linear complementarity constraints, Math. Programming, 128(2011), 1-18.

  53. X. Chen, A. Frommer and B. Lang, Computational Existence Proofs for Spherical t-Designs , Numerische Mathematik, 117(2011), 289-305.

  54. C. An, X. Chen, I.H. Sloan, R. S. Womersley, Well conditioned spherical designs for integration and interpolation on the two-Sphere, SIAM J. Numerical Analysis , 48(2010), 2135-2157.

  55. X.Chen, F. Xu and Y. Ye, Lower bound theory of nonzero entries in solutions of l_2-l_p minimization, SIAM J. Scientific Computing, 32(2010), 2832-2852.

  56. X. Chen and W. Zhou, Smoothing Nonlinear Conjugate Gradient Method for Image Restoration using Nonsmooth Nonconvex Minimization, SIAM J. Imaging Sciences 3(2010), pp. 765-790.

  57. S. Xiang, X. Chen and H. Wang, Error bounds for approximation in Chebyshev points, Numerische Mathematik, 116(2010) 463-491.

  58. W. Zhou and X. Chen, Global convergence of a new hybrid Gauss-Newton structured BFGS method for nonlinear least squares problems, SIAM J. Optimization, 20(2010) 2422-2441.

  59. C. Zhang and X. Chen, Smoothing projected gradient method and its application to stochastic linear complementarity problems, SIAM J. Optimization 20(2009) 627-649.

  60. X. Chen and J. Ye, A class of quadratic programs with linear complementarity constraints, Set-Valed and Variational Analysis 17(2009) 113-133.

  61. T, Kimura and X. Chen, Validated solution of saddle point linear systems, SIAM J. Matrix Anal. Applications 30(2009) 1697-1708.

  62. X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems , Mathematical Programming 117(2009) 51-80

  63. Y Shi, Y. Tian, X. Chen, and P. Zhang, Regularization mulitiple criteria linear programs for classification, Science in China Series F: Information Sciences. 52(2009) 1812-1820.

  64. C. Zhang, X. Chen and N. Xiu, Global error bounds for the extended vertical LCP, Computational Optimization and Applications 42(2009) 335-352

  65. X. Chen, Numerical verification method for spherical t-designs, Japan Journal of Industrial and Applied Mathematics, 26(2009) 317-325.

  66. 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

  67. X. Chen and S. Mahmoud, Implicit Runge-Kutta methods for Lipschitz continuous ordinary differential equations , SIAM J. Numer. Anal. 46(2008) 1266-1280

  68. G. Alefeld and X. Chen, A regularized projection method for complementarity problems with non-Lipschitzian functions, Mathematics of Computation 77(2008) 379-395

  69. 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

  70. X. Chen and S. Xiang, Perturbation bounds of P-matrix linear complementarity problems , SIAM J. Optimization 18(2007) 1250-1265.

  71. 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.

  72. H. Fang, X. Chen and M. Fukushima, Stochastic R0 matrix linear complementarity problems , SIAM J. Optimization 18(2007) 482-506.

  73. 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

  74. X. Chen and T. Kimura, Finite element surface fitting for bridge management, International J. Information Technology & Decision Making (2006) 671-681

  75. X. Chen and S. Xiang, Computation of error bounds for P-matrix linear complementarity problem , Mathematical Programming 106(2006) 513-525.

  76. X. Chen and M. Fukushima, Expected Residual Minimization Method for Stochastic Linear Complementarity Problems, Mathematics of Operations Research 30(2005) 1022-1038.

  77. X. Chen, Finite Difference Smoothing Solution of Nonsmooth Constrained Optimal Control Problems , Numerical Functional Analysis and Optimization 26(2005) 49-68

  78. 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.

  79. X. Chen, First order conditions for nonsmooth discretized constrained optimal control problems, SIAM J Control and Optimazation, 42(2004) 2004-2015.

  80. X. Chen and K. Hashimoto, Numerical validation of solutions of saddle point matrix equations, Numerical Linear Algebra with Applications, 10(2003) 661-672.

  81. 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.

  82. X. Chen and K. Hashimoto Verication methods for nonlinear equations with saddle point functions, Journal of Computational and Applied Mathematics, 159(2003),13-24.

  83. 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.

  84. 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.

  85. X. Chen, Applications of smoothing methods in numerical analysis and optimization, Journal of Asian Information Science Life, 1(2002), 1-13.

  86. G.E. Alefeld, X. Chen, F.A.Potra, Numerical validation of solutions of complementarity problems: the nonlinear case, Numerische Mathematik, 92(2002) 1-16.

  87. X. Chen, L. Qi and Y. Yang, Lagrangian globalization methods for nonlinear complementarity problems, Journal of Optimization Theory and Applications, 112(2002) 77-95.

  88. X. Chen, On convergence of SOR methods for nonsmooth equations, Numerical Linear Algebra with Applications, 9(2002)81-92.

  89. 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.

  90. X. Chen, A superlinearly and globally convergent method for reaction and diffusion problems with a non-Lipschitzian operator, Computing[Suppl], 15(2001) 79-90.

  91. 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.

  92. X. Chen and Y. Ye, On smoothing methods for the P_0 matrix linear complementarity problem, SIAM J. Optimization. 11(2000) 341-363.

  93. X. Chen, Z. Nashed and L. Qi, Smoothing methods and semismooth methods for nondifferentiable operator equations SIAM J. Numerical Analysis. 38 (2000) 1200-1216.

  94. X. Chen, Newton-type methods for stochastic programming, Mathematical and Computer Modelling. 31 (2000) 89-98.

  95. B. Chen, X. Chen and C. Kanzow, A penalized Fischer-Burmeister NCP-function, Mathematical Programming. 88 (2000) 211-216.

  96. X. Chen, Smoothing methods for complementarity problems and their applications: a survey, Journal of the Operations Research Society of Japan, 43(2000) 32-47.

  97. 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.

  98. 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.

  99. G.E. Alefeld, X. Chen and F.A. Potra, Numerical validation of solutions of linear complementarity problems Numerische Mathematik, 83 (1999) 1-23 .

  100. 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.

  101. X. Chen and Y. Ye, "On homotopy-smoothing methods for variational inequalities", SIAM J. Control and Optimization, 37 (1999) 587-616.

  102. X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Math. Programming, 85(1999) 313-334.

  103. X. Chen, "On preconditioned Uzawa Methods and SOR methods for saddle point problems" J. Comp. Appl. Math. 100(1998) 207-224.

  104. 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.

  105. 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.

  106. X. Chen, "A verification method for solutions of nonsmooth equations", Computing, 58(1997) 281-294. .

  107. 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.

  108. X. Chen, "Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations", J. Comp. & Appl. Math. 80(1997),105-126.

  109. L. Qi and X. Chen, "A preconditioning proximal Newton method for nondifferentiable convex optimization", Math. Programming, 79(1997) 411-429.

  110. 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.

  111. 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.

  112. X. Chen, "Convergence of the BFGS method for LC1 constrained optimization", SIAM J. Control and Optim., 34(1996) 2051-2063

  113. X. Chen and R.S. Womersley, "A parallel inexact Newton method for stochastic programs with recourse", Annals of Operations Research, 64(1996), 113-141.

  114. 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.

  115. 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.

  116. L. Qi and X. Chen, "A globally convergent successive approximation method for severely nonsmooth equations", SIAM J. Control and Optimization, 33 (1995), 402-418.

  117. 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.

  118. X. Chen and T. Yamamoto, "Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable term", J. Comp. Appl. Math., 55(1994), 311-324.

  119. M.Z. Nashed and X. Chen, "Convergence of Newton-like methods for singular operator equations using outer inverses", Numer. Math., 66(1993), 235-257.

  120. X. Chen and T. Yamamoto, A convergence ball for multistep simplified Newton-like methods, Numerical Functional Analysis and Optimization, 14(1993), 15-24.

  121. X. Chen and T. Yamamoto, On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators, Computing, 49(1992), 87-94.

  122. X. Chen and T. Yamamoto, PCG methods applied to a system of nonlinear equations, Journal Computational and Applied Mathematics, 38(1991), 61-75.

  123. 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.

  124. 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.

  125. 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.

  126. T. Yamamoto and X. Chen, Validated methods for solving nonlinear systems, Information Processing, 31(1990), 1191-1196.

  127. X. Chen and D. Wang, On the optimal properties of the Krawczyk-type interval operator, International Journal of Computer Mathematics, 29(1989), 235-245.

  128. X. Chen and T. Yamamoto, Convergence domains of certain iterative methods for solving nonlinear equations, Numerical Functional Analysis and Optimization, 10(1989), 37-48.

  129. 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.

  130. Z. You and X. Chen, Interval iterative methods for nonlinear numerical equations under partial ordering (II), Journal of Computational Mathematics, 6(1988), 318-324.

  131. Z. You and X. Chen, Interval iterative methods for nonlinear numerical equations under partial ordering(I), Journal of Computational Mathematics, 6(1988), 39-47.

  132. 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.

  133. Z. You and X. Chen, A continuation-interval method for nonlinear systems, Science Bulletin, 33(1987), 270-273.

  134. 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.

  135. Z. You and X. Chen, On two-sided interval relaxation methods, Science Bulletin, 31(1986), 1521-1524.

  136. 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.

  137. 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.

  138. D. Wang and X. Chen, Interval relaxation methods for nonlinear systems of nonlinear equations, Mathematics Numerical Sinica, 7(1985), 426-432.

  139. 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.

  140. Z. You and X. Chen, A decomposition coordination algorithm for a large-scale programming, Mathematics Numerical Sinica, 7(1985), 247-252.

  141. 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.

  142. X. Chen, An improved D.S.C. algorithm, Science Bulletin, 20(1983), 1276.


Reports


Hirosaki University

UNSW