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