"Everything should be made as simple as possible, but not simpler." - Albert Einstein

• Call for submission: 2011-12 HKMS Best Thesis Award

• 2012 HKBU Spring Workshop on Optimization, January 09, 2012, FSC1217, HKBU.

• Chapter 1    (Matlab Code)  (Homework, Due on Feb 21,2012)
• Chapter 2

•  Ng M. K., Yuan X. M. and  Zhang W. X., On variational image decomposition model for blurred images with missing pixel values;
•  He B. S. and Yuan, X. M., On nonergodic convergence rate of Douglas-Rachford alternating direction method of multipliers [PDF];
•  Chan R. H., Tao M., and Yuan X.M., Constrained total variational deblurring models and fast algorithms based on alternating direction method of multipliers; 
•  He B. S. and Yuan X. M., On convergence rate of the Douglas-Rachford operator splitting method [PDF] [Revised Version];
•  Han D. R., He H.J., Yang H. and Yuan X. M., A customized Douglas-Rachford splitting algorithm for separable convex minimization with linear constraints;
•  He B. S., Tao M. and Yuan X. M., On the O(1/t) convergence rate of Eckstein and Bertsekas's generalized alternating direction method of multipliers [PDF];
•  He B. S and Yuan X. M., Linearized alternating direction method with Gaussian back substitution for separable convex programming [PDF];
•  Tao M and Yuan X. M, On the O(1/t) convergence rate of alternating direction method with logarithmic-quadratic proximal regularization [PDF] [Revised Version];
•  Cai X. J., Gu G. Y., He B. S. and Yuan X.M., A relaxed customized proximal point algorithm for separable convex programming [PDF];
•  Chan R. H., Tao M., and Yuan X.M., Linearized alternating direction method for constrained linear least-squares problem;
•  Han D.R., Yuan X.M. and Zhang W.X., An augmented-Lagrangian-based parallel splitting method for separable convex programming with applications to image processing;

• Xiao Y. H., Yang J. F. and Yuan, X. M., Alternating algorithms for total variation image reconstruction from random projections, Inverse Problems and Imaging; 
• He B.S., Tao M. and Yuan X.M., A splitting method for separable convex programming, IMA Journal of Numerical Analysis;
• He B.S. , Yuan X.M. and Zhang W.X., A customized proximal point algorithm for convex minimization with linear constraints,Computational Optimization with Applications; 
• Wang X. F. and Yuan X. M., The linearized alternating direction method for Dantzig Selector, SIAM Journal on Scientific Computing
• Yang W. H and Yuan, X. M., The GUS-property of second-order cone linear complementarity problems, Mathematical Programming;
• Han. D. R., Yuan X. M., Zhang W. X and Cai X. J., An ADM-based splitting method for separable convex programming, Computational Optimization with Applications;

• He B.S., Tao M. and Yuan X.M., Alternating direction method with Gaussian back substitution for separable convex programming, SIAM Journal on Optimization;
• He B. S and Yuan X. M., On the O(1/n) convergence rate of Douglas-Rachford alternating direction method [PDF], SIAM Journal on Numerical Analysis;
• Han D. R and Yuan X. M, A note on the alternating direction method of multipliers, Journal of Optimization Theory and Applications;
• He B. S and Yuan X. M., Forward-backward-based descent methods for composite variational inequalities, Optimization Methods and Software;
• Jiang J.L. and Yuan X.M., Minimax location with farthest Euclidean distances, Pacific Journal on Optimization;
• He B.S. and Yuan X.M., An accelerated inexact proximal point algorithm for convex minimization, Journal of Optimization Theory and Applications;
• Yang J.F. and Yuan X.M., Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization, Mathematics of Computation;
• He B.S., Xu M.H., Tao M. and Yuan X.M., Alternating directions based contraction method for generally separable linearly constrained convex programming problems, Optimization;
• Zhang W. X., Han D. R and Yuan X. M., An efficient simultaneous method for constrained multiple-sets split feasibility problem, Computational Optimization with Applications;
• Yuan X.M., Alternating direction method of multipliers for covariance selection models, Journal of Scientific Computing;
• Tao M and Yuan X. M., Inexact parallel splitting augmented Lagrangian methods for monotone variational inequalities with separablestructures, Computational Optimization with Applications;
• He B.S. and Yuan X.M., The uniform framework of some proximal-based decomposition methods for monotone variational inequalities with separable structure, Pacific Journal of Optimization;
• Yuan X.M. and Yang J.F., Sparse and low-rank matrix decomposition via alternating direction methods, Pacific Journal of Optimization;
• Jiang J.L. and Yuan X.M., A heuristic algorithm for locating multiple facilities with regional demand, Computational Optimization with Applications;
• Li M. and Yuan X.M., Some proximal algorithms for linearly constrained general variational inequalities, Optimization;

• He B.S. and Yuan X.M., Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective, SIAM Journal on Imaging Science, 5 (1), 119-149, 2012;
• Chen C.H., He B.S. and Yuan X.M., Matrix completion via alternating direction methods, IMA Journal of Numerical Analysis, 32, 227-245,2012;

• Yuan X.M. and Li M., An LQP-based decomposition method for solving a class of variational inequalities, SIAM Journal on Optimization, 21(4), 1309–1318, 2011;
• Chan R.H., Yang J.F. and Yuan X.M., Alternating direction method for image inpainting in wavelet domain, SIAM Journal on Imaging Science,4, 807-826,2011;
• Ng M.K., Wang F. and Yuan X.M., Inexact alternating direction methods for image recovery, SIAM Journal on Scientific Computing;, 33(4), 1643-1668, 2011;
• Yuan X.M., An improved proximal alternating direction method for structured variational inequalities, Computational Optimization and Applications, 49(1), 17-29, 2011;
• Tao M. and Yuan X.M., Recovering low-rank and sparse components of matrices from incomplete and noisy observations, SIAM Journal on Optimization, 21 (1), 57-81, 2011;
• He B.S., Xu M.H. and Yuan X.M. , Solving large-scale least squares covariance matrix problems by alternating direction methods, SIAM Journal of Matrix Analysis and Applications, 32(1), 136-152, 2011;
• Li M., Liao L. Z. and Yuan X.M., Some Goldstein's type methods for co-coercive variant variational inequalities, Applied Numerical Mathematics, 61, 216-228, 2011;
• Ng M.K., Wang F. and Yuan X.M., Fast minimization methods for solving constrained total-variation superresolution image reconstruction, Multidimensional Systems and Signal Processing, 22, 259-286, 2011;
• Han D.R. and Yuan X.M., Existence of anonymous link tolls for oligopolistic games and the efficiency analysis, Journal of Industrial and Management Optimization, 7(2), 347-364, 2011;
• Tao M., Yuan X.M. and He B.S., Solving a class of matrix minimization problems by linear variational inequality approaches, Linear Algebra and Applications, 434, 2343–2352, 2011;
• He B.S., Xu W., Yang H., Yuan X.M., Solving resource protection and supply guarantee problems in economic equilibria, Networks and Spatial Economics,11, 127-138, 2011;

• Ng M.K., Weiss P.A and Yuan X.M., Solving constrained total-variation image reconstruction problems via alternating direction methods, SIAM Journal on Scientific Computing, 32(5), 2710-2736, 2010;
• Jiang Z. K. and Yuan X.M., New parallel descent-like method for solving a class of variational inequalities, Journal of Optimization Theory and Applications, 145(2), 311-323, 2010;
• Han D.R., Yang H. and Yuan X.M., A practical trial-and-error implementation of marginal-cost pricing on networks, Journal of Industrial and Management Optimization, 6(2), 299-313, 2010;
• Han D.R., Yang H and Yuan X.M., The efficiency analysis for oligopolistic games with nonseparable cost functions, International Journal of Mathematical Modelling and Numerical Optimization, 1(3), 237-257, 2010;
• Li M. and Yuan X.M., An improved LQP-based method for nonlinear complementarity problems, Frontiers of Mathematics in China, 51(1), 23-35, 2010;

• Li M., Liao L. Z. and Yuan X.M., Proximal point algorithms for general variational  inequalities, Journal of Optimization Theory and Applications, 142(1), 125-145, 2009;
• Bauschke H., Wang S., Ye J. and Yuan X.M., Bregman distance and Chebyshev sets, Journal of Approximation Theory, 159(1), 3-25, 2009;
• Bauschke H., Wang S., Ye J. and Yuan X.M., Bregman distance and Klee sets, Journal of Approximation Theory, 158(2), 170-183, 2009;

• Yuan X.M., A new criterion for the inexact Logarithmic-Quadratic Proximal method and its derived hybrid methods, Journal of Global Optimization, 40(4), 529-543 2008;
• Li M. and Yuan X.M., An improved Goldstein's type method for a class of variant variational inequalities, Journal of Computational and Applied Mathematics, 214(1), 304-312, 2008;
• Li M., Liao L. Z. and Yuan X.M., A modified projection method for co-coercive variational inequalities, European Journal of Operational Research, 189(2), 310-323, 2008;
• Shao H., Lam W.H.K., Tam M.L. and Yuan X.M., Modeling rain effect on risk-taking behaviours on multi-classes in road network with uncertainty, Journal of Advanced Transportation, 42(3), 265-290, 2008;
• Li M. and Yuan X.M., An APPA-based descent method with optimal step-sizes for monotone variational inequalities, European Journal of Operational Research, 186, 486-495, 2008;
• Jiang J. L. and Yuan X.M., A heuristic algorithm for constrained multi-source Weber problem--the variational approach, European Journal of Operational Research, 187, 357-370, 2008;
  

• Bnouhachem A.and Yuan X.M., An extended LQP method for monotone nonlinear complementarity problems, Journal of Optimization Theory and Applications, 135, 343-353, 2007;
• Li M. and Yuan X.M., An improved proximal-based decomposition method for structured monotone variational inequalities, Applied Mathematics and Mechanics,  28(12),1659-1668, 2007;
• Xu M.H., Yuan X.M. and Huang Q., An improved general extra-gradient method with refined step size for nonlinear monotone variational inequalities, Journal of Global Optimization; 39, 343-353,2007;
• Yuan X.M., The prediction-correction approach to nonlinear complementarity problems, European Journal of Operational Research, 176(3), 1357-1370,2007;
• Ye C.H. and Yuan X.M., A descent method for structured monotone variational inequalities, Optimization Methods and Software, 22 , 329-338,2007;

• He B.S., Xu Y. and Yuan X.M., An Logarithmic-Quadratic Proximal prediction-correction method for structured monotone variational inequalities, Computational Optimization and Applications, 35(1), 19-46, 2006;
• Yuan X.M. and Zhou L., An improved extra-gradient method for minimizing a sum of p-norms: a variational inequality approach, Computational Optimization and Applications, 34(3) , 321-341, 2006;
• He B.S., Liao L. Z. and Yuan X.M., A LQP method-based interior prediction-correction method for nonlinear complementarity problems, Journal of Computational Mathematics; 24(1), 33-44,2006;
• Xu Y., He B.S. and Yuan X.M., A hybrid logarithmic-quadratic proximal method for nonlinear complementarity problems, Journal of Mathematical Analysis and Applications, 322 , 276-287,2006;

• Yuan X.M., The improvement with relative errors of He et al's inexact alternating direction methods for monotone variational inequalities, Mathematics and Computers Modeling, 42, 1225-1236, 2005;
  

• He B.S., Yang Z.H. and Yuan X.M., An approximate proximal-extragradient type method for monotone variational inequalities, Journal of Mathematical Analysis and Applications, 300(2), 362-374, 2004;
• He B.S., Yuan X.M. and Zhang J.Z., Comparison of two kinds of prediction-correction methods for monotone variational inequalities, Computational Optimization and Applications, 27 (3), 247-267,2004.

• Splitting methods for separable convex programming, 2011-2014, Principal Investigator;
• Numerical algorithms for some low-rank-driven optimization problems, 2010-2013, Principal Investigator;
• The variational inequality approach to solving large-scale matrix optimization problems, 2009-2011, Principal Investigator;
  

• Complexity analysis and acceleration of proximal point algorithm and augmented Lagrangian method, 2011-2012, Principal Investigator;
• Efficiency analysis for some oligopolistic games, 2010-2011, Principal Investigator;
• Some numerical algorithms for general variational inequalities, 2009-2010, Principal Investigator;
  

• Numerical algorithms for solving a class of structured variational inequalities, 2008-2010, Principal Investigator;
• Disruption management and robust optimization, Key Project of National Science Foundation of China, 2008-; (resignned at 2008 Aug), Co-PI;

• Intelligent techniques for zoning traffic network dynamically: based on traffic flow characteristics, The National High Technology Research and Development Program of China (well-known as 863 Programme), 2007-2008, Co-PI;
  

• LQP-based descent methods for variational inequalities,  Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, 2008-2009, Principal Investigator;