LIAO, Li-Zhi

BSc, Tsinghua; MSc, PhD, Cornell
Professor
Department of Mathematics
Hong Kong Baptist University
Kowloon Tong, Hong Kong
Research Interests:
Continuous Method for Optimization, Theory and Computation of Optimization and Optimal Control, Parallel Computing
Telephone: (852) 3411-7022
Facsimile: (852) 3411-5811
Email:
Office: FSC1215, HKBU
Recent Publications:
  1. X. B. Gao and L.-Z. Liao, Novel continuous- and discrete-time neural networks for solving quadratic minimax problems with linear equality constraintsIEEE, TNNLS, (to appear).
  2. L. Hou, D. Chu, and L.-Z. Liao, A progressive hierarchical alternating least squares method for symmetric nonnegative matrix factorization, IEEE PAMI, 45 (5), 5355-5369, 2023.
  3. L. Hou and L.-Z. Liao, An interior point parameterized central path following algorithm for linearly constrained convex programming, JSC, 90 (3), 1-31, 2022.
  4. Y. Ma and L.-Z. Liao, The Glowinski-Le Tallec splitting method revisited: A general convergence and convergence rate analysis, JIMO, 17 (4), 1681-1711, 2021.
  5. X. Qian, L.-Z. Liao, and J. Sun, A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming, Math. Prog., Vol. 179 (1-2), 1-19, 2020.
  6. L. M. Sun and L.-Z. Liao, An interior point continuous path-following trajectory for linear programming, JIMO, 15(4), 1517-1534, 2019.
  7. H. Zhu, L.-Z. Liao, and M. K. Ng, Multi-instance dimensionality reduction via sparsity and orthogonality, Neural Comput., 30(12), 3281-3308, 2018.
  8. H. W. Yue, L.-Z. Liao, and X. Qian, Two interior point continuous trajectory models for convex quadratic programming with bound constraints, PJO, 14(3), 527-550, 2018.
  9. H. Zhu, C. Chen, L.-Z. Liao, and M. K. Ng, Multiple graphs clustering by gradient flow method, J. Franklin Institute, 355(4), 1819-1845, 2018.
  10. X. Qian, L.-Z. Liao, J. Sun, and H. Zhu, The convergent generalized central paths for linearly constrained convex programming, SIAM J. Optim., 28(2), 1183-1204, 2018.
  11. X. Qian and L.-Z. Liao, Analysis of the primal affine scaling continuous trajectory for convex programming, PJO, 14(2), 261-272, 2018.
  12. J. Sun, L.-Z. Liao, and B. Rodrigues, Quadratic two-stage stochastic optimization with coherent measures of risk, Math. Prog., B, 168 (1-2), 599-613, 2018.
  13. X. B. Gao and L.-Z. Liao, A novel neural network for generally constained variational inequalities, IEEE TNNLS, 28 (9), 2062-2075, 2017.
  14. H. Zhu, X. Zhang, D. Chu, and L.-Z. Liao, Noncovex and nonconvex optimization with generalized orthogonality constraints: an approximate augmented Lagrangian method, J. Sci. Comput. 72, 331-372, 2017.
  15. X. Qian, L.-Z. Liao, and J. Sun, Analysis of some interior point continuous trajectories for convex programming, Optimization, 66 (4), 589-608, 2017.
  16. X. W. Zhang, L. Chen, D. Chu, L.-Z. Liao, M. K. Ng, and C. E. Tan, Incremental regularized least squares for dimensionality reduction of large-scale data, SISC, 38 (3), B414-439, 2016.
  17. D. Chu, L.-Z. Liao, M. K. Ng, and X. Y. Wang, Incremental linear discriminant analysis: a fast algorithm and comparison, IEEE TNNLS, 26 (11), 2716-2735, 2015.
  18. L.-Z. Liao, A study of the dual affine scaling continuous trajectories for linear programming, JOTA, 163 (2), 548-568, 2014.
  19. L. H. Zhang, W. H. Yang, and L.-Z. Liao, A note on the trace quotient problem, Optim. Lett., 8 (5), 1637-1645, 2014.
  20. L. H. Zhang, W. H. Yang, and L.-Z. Liao, On an efficient implementation of the face algorithm for linear programming, JCM, 31 (4), 335-354, 2013.
  21. D. Chu, L.-Z. Liao, M. K. Ng, and X. W. Zhang, Sparse canonical correlation analysis: new formulation and algorithm, IEEE, TPAMI, 35 (12), 3050-3065, 2013.
  22. M. Li, L.-Z. Liao, and X. M. Yuan Inexact alternating direction methods of multipliers with logarithmic-quadratic proximal regularization, JOTA, 159 (2), 412-436, 2013.
  23. L. H. Zhang, L.-Z. Liao, and M. K. Ng, Superlinear convergence of a general algorithm for the generalized Foley-Sammon discriminant analysis, JOTA, 157 (3), 853-865, 2013.
  24. C. T. Kelley and L.-Z. Liao, Explicit pseudo-transient continuation, PJO, 9 (1), 77-91, 2013.
  25. D. Chu, L.-Z. Liao, and M. K. Ng, Sparse orthogonal linear discriminant analysis, SISC, 34 (5), 2421-2443, 2012.
  26. L. H. Zhang and L.-Z. Liao, An alternating variable method for the maximal correlation problem, JOGO, 54 (1), 199-218, 2012.
  27. W.-K. Ching, D. Chu, L.-Z. Liao, and X. Wang, Regularized orthogonal linear discriminant analysis, Patten Recognition, 45, 2719-2732, 2012.
  28. B. S. He, L.-Z. Liao, and X. Wang, Proximal-like contraction methods for monotone variational inequalities in a unified framework I: effective quadruple and primary methods, COAP, 51 (2), 649-679, 2012.
  29. B. S. He, L.-Z. Liao, and X. Wang, Proximal-like contraction methods for monotone variational inequalities in a unified framework II: general methods and numerical experiments, COAP, 51 (2), 681-708, 2012.
  30. X. B. Gao and L.-Z. Liao, Stability and convergence analysis for a class of neural networks, IEEE TNN, 22 (11), 1770-1782, 2011.
  31. M. K. Ng, L.-Z. Liao, L. H. Zhang, On sparse linear discriminant analysis algorithm for high-dimentional data classification, Num. Lin. Alg. Appl., 18 (2), 223-235, 2011.
  32. L. H. Zhang, L.-Z. Liao, and L. M. Sun, Towards the global solution of the maximal correlation problem, JOGO, 49 (1), 91-107, 2011.
  33. M. Li, L.-Z. Liao, and X. M. Yuan, Some Goldstein's type methods for co-coersive variant variational inequalities, Appl. Num. Math., 61, 216-228, 2011.
  34. L. H. Zhang, L.-Z. Liao, and M. K. Ng, Fast algorithms for the generalized Foley-Sammon discriminant analysis, SIMAX, 31 (4), 1584-1605, 2010.
  35. X. B. Gao and L.-Z. Liao, A new one-layer neural network for linear and quadratic programming, IEEE TNN, 21 (6), 918-929, 2010.
  36. X. Wang, B. S. He, and L.-Z. Liao, Steplengths in the extragradient type methods, JCAM, 233 (11), 2925-2939,2010.
  37. M. Li, L.-Z. Liao, and X. M. Yuan, Proximal point algorithms for general variational inequalities, JOTA, 142 (1), 125-145, 2009.
  38. X. B. Gao and L.-Z. Liao, A new projection-based neural network for constrained variational inequalities, IEEE TNN, 20 (3), 373-388, 2009.
  39. X. L. Luo, C. T. Kelley, L.-Z. Liao, and H. W. Tam, Combining trust-region techniques and Rosenbrock methods to compute stationary points, JOTA, 140 (2), 265-286, 2009.
  40. B. S. He, M. Li, and L.-Z. Liao, An improved contraction method for structured monotone variational inequalities, Optimization, 57 (5), 643-653, 2008.
  41. L. H. Zhang and L.-Z. Liao, A generalized projective dynamic for solving extreme and interior eigenvalue problems, DCDS-B, 10 (4), 997-1019, 2008.
  42. C. T. Kelley, L.-Z. Liao, L. Q. Qi, M. T. Chu, J. P. Reese, and C. Winton, Projected pseudotransient continuation, SINUM, 46 (6), 3071-3083, 2008.
  43. M. Li, L.-Z. Liao, and X. M. Yuan, A modified projection method for co-coercive variational inequalities, EJOR, 189 (2), pp. 310-323, 2008.
  44. X. B. Gao, G. H. Golub, and L.-Z. Liao, Continuous methods for symmetric generalized eigenvalue problems LAA, Vol. 428 (2-3), pp. 676-696, 2008.
  45. L. H. Zhang, C. T. Kelley, and L.-Z. Liao, A continuous Newton-type method for unconstrained optimization Pacific Journal of Optimization, 4 (2), pp. 259-277, 2008.
  46. X. L. Luo, L.-Z. Liao, and H. W. Tam, Convergence analysis of the Levenberg-Marquardt method, Optimization Methods and Software, 22 (4), pp. 659-678, 2007.
  47. B. S. He, L.-Z. Liao, M. J. Qian,Alternating projection based prediction-correction methods for structured variational inequalities, J. Comput. Math, 24 (6), pp. 693-710, 2006.
  48. X. B. Gao and L.-Z. Liao, A novel neural network for a class of convex quadratic minimax problems, Neural Computation, Vol. 18 (8), pp. 1818-1846, 2006.
  49. G. H. Golub and L.-Z. Liao, Continuous methods for extreme and interior eigenvalue problems, LAA, Vol. 415, pp. 31-51, 2006.
  50. B. S. He, L.-Z. Liao, and X. M. Yuan, A LQP based interior prediction-correction method for nonlinear complementarity problems, J. Comput. Math, 24 (1), pp. 33-44, 2006.
  51. X. B. Gao, L.-Z. Liao, and L. Q. Qi, A novel neural network for variational inequalities with linear and nonlinear constraints, IEEE Trans. Neural Networks, Vol. 16 (6), pp. 1305-1317, 2005.
  52. L.-Z. Liao, L. Q. Qi, and H. W. Tam, A gradient-based continuous method for large-scale optimization problems, Journal of Global Optimization, 31, pp. 271-286, 2005.
  53. L.-Z. Liao, A continuous method for convex programming problems,, JOTA, 124 (1): 207-226, 2005.
  54. X. B. Gao, L.-Z. Liao, and W. M. Xue, A neural network for a class of convex quadratic minimax problems with constraints, IEEE Trans. Neural Networks, 15 (3), pp. 622-628, 2004.
  55. Y.-H. Dai, L.-Z. Liao, and D. Li, On restart procedures for the conjugate gradient method, Numerical Algorithms, 35 (2-4), pp. 249-260, 2004.
  56. L.-Z. Liao, H. D. Qi, and L. Q. Qi, Neurodynamical optimization, Journal of Global Optimization, 28, pp. 175-195, 2004.
  57. L.-Z. Liao and S. L. Wang, A self-adaptive projection and contraction method for linear complementarity problems, App. Math. Optim., 48 (3), pp. 169-180, 2003.
  58. B. S. He, L.-Z. Liao, and S. L. Wang, Self-adaptive operator splitting methods for monotone variational inequalities, Numer. Math., 94 (4), pp. 715-737, 2003
  59. B. S. He, L.-Z. Liao, and Z. H. YangA new approximate proximal point algorithm for maximal monotone operator, Science in China, Series A, 46 (2), pp. 200-206, 2003.
  60. X. B. Gao and L.-Z. Liao, A neural network for monotone variational inequalities with linear constraints, Physics Letters A, 307 (2-3), pp. 118-128, 2003.
  61. C. K. Ng, L.-Z. Liao, and D. Li, A globally convergent and efficient method for unconstrained discrete-time optimal control, Journal of Global Optimization, 23 (3-4), pp. 401-421, 2002.
  62. L.-Z. Liao and D. Li, Adaptive differential dynamic programming for multiobjective optimal control, Automatica, 38 (6), pp. 1003-1015, 2002.
  63. B. S. He, L.-Z. Liao, D. R. Han, and H. Yang, An new inexact alternating directions method for monotone variational inequalities, Math. Prog. 92 (1), pp. 103-118, 2002.
  64. X. S. Zhang, J. L. Zhang, and L.-Z. Liao, An adaptive trust region method and its convergence, Science in China (Series A), 45 (5), pp. 620-631, 2002.
  65. B. S. He and L.-Z. Liao, Improvements of some projection methods for monotone nonlinear variational inequalities, Journal of Optimization Theory and Applications, 112 (1), pp. 111-128, 2002.
  66. L.-Z. Liao and S. L. Wang, A self-adaptive projection and contraction method for monotone symmetric linear variational inequalities, Computers & Mathematics with Applications, 43 (1-2), pp. 41-48, 2002.
  67. Y.-H. Dai and L.-Z. Liao, R-linear convergence of the Barzilai and Borwein gradient method, IMA Journal of Numerical Analysis, 22 (1), pp. 1-10, 2002.
  68. L.-Z. Liao, H. D. Qi, and L. Q. Qi, Solving nonlinear complementarity problems with neural networks: a reformulation method approach, JCAM, 131 (1-2), pp. 343-359, 2001.
  69. D. Z. Cheng, W. M. Xue, L.-Z. Liao, and D. Y. Cai, On generalized Hamiltonian systems, Acta Mathematicae Applicatae Sinica, Vol. 17 (4), pp. 475-483, 2001.
  70. S. L. Wang and L.-Z. Liao, Decomposition method with a variable parameter for a class of monotone variational inequality problems, Journal of Optimization Theory and Applications, Vol. 109 (2), pp. 415-429, 2001.
  71. Q. M. Han, L.-Z. Liao, H. D. Qi, and L. Q. Qi, Stability analysis of gradient-based neural networks for optimization problems, Journal of Global Optimization, 19 (4), pp. 363-381, 2001.
  72. Y. H. Dai and L.-Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Applied Mathematics & Optimization, 43 (1), pp. 87-101, 2001.
  73. H. D. Qi and L.-Z. Liao, A smoothing Newton method for general nonlinear complementarity problems, Computational Optimization and Applications, 17 (2-3), pp. 231-253, 2000.
  74. L.-Z. Liao and D. Li, Successive method for general multiple linear-quadratic control problem in discrete-time, IEEE Trans. Automat. Contr., 45 (7), pp. 1380-1385, 2000.
  75. H. D. Qi and L.-Z. Liao, A smoothing Newton method for extended vertical linear complementarity problems, SIAM J. Matrix Anal. Appl., 21 (1), pp. 45-66, 1999.
  76. B. S. He, L.-Z. Liao, and H. Yang, A Decomposition Method for a Class of M onotone Variational Inequality Problems, Journal of Optimization Theory and Applications, 103 (3), pp. 603-622, 1999.
  77. L.-Z. Liao, A recurrent neural network for N-stage optimal control problems, Neural Processing Letters, 10 (3), pp. 195-200, 1999.
  78. L.-Z. Liao and H. Qi, A neural network for the linear complementarity problem, Mathl. Comput. Modelling, 29 (3), pp. 9-18, 1999.
  79. H. D. Qi, L.-Z. Liao, and Z.-H. Lin, Regularized smoothing approximations to vertical nonlinear complementarity problems, J. Math. Anal. Appl., 230, pp. 261-276, 1999.
  80. C. Mansfield, C. A. Shoemaker, and L.-Z. Liao, Utilizing sparsity in time varying optimal control of aquifer cleanup, ASCE J. Water Resour. Plan. and Mang., 124, pp. 15-21, 1998.