Kowloon Tong, Hong Kong

Continuous Method for Optimization, Theory and Computation of Optimization and Optimal Control, Parallel Computing

- Y. Ma and L.-Z. Liao,
*The Glowinski-Le Tallec splitting method revisited: A general convergence and convergence rate analysis*, JIMO, (to appear). - 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. - L. M. Sun and L.-Z. Liao,
*An interior point continuous path-following trajectory for linear programming*, JIMO, 15(4), 1517-1534, 2019. - H. Zhu, L.-Z. Liao, and M. K. Ng,
*Multi-instance dimensionality reduction via sparsity and orthogonality*, Neural Comput., 30(12), 3281-3308, 2018. - 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. - 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. - 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. - X. Qian and L.-Z. Liao,
*Analysis of the primal affine scaling continuous trajectory for convex programming*, PJO, 14(2), 261-272, 2018. - 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. - X. B. Gao and L.-Z. Liao,
*A novel neural network for generally constained variational inequalities*, IEEE TNNLS, 28 (9), 2062-2075, 2017. - 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. - X. Qian, L.-Z. Liao, and J. Sun,
*Analysis of some interior point continuous trajectories for convex programming*, Optimization, 66 (4), 589-608, 2017. - 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. - 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. - L.-Z. Liao,
*A study of the dual affine scaling continuous trajectories for linear programming*, JOTA, 163 (2), 548-568, 2014. - L. H. Zhang, W. H. Yang, and L.-Z. Liao,
*A note on the trace quotient problem*, Optim. Lett., 8 (5), 1637-1645, 2014. - 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. - 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. - 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. - 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. - C. T. Kelley and L.-Z. Liao,
*Explicit pseudo-transient continuation*, PJO, 9 (1), 77-91, 2013. - D. Chu, L.-Z. Liao, and M. K. Ng,
*Sparse orthogonal linear discriminant analysis*, SISC, 34 (5), 2421-2443, 2012. - L. H. Zhang and L.-Z. Liao,
*An alternating variable method for the maximal correlation problem*, JOGO, 54 (1), 199-218, 2012. - W.-K. Ching, D. Chu, L.-Z. Liao, and X. Wang,
*Regularized orthogonal linear discriminant analysis*, Patten Recognition, 45, 2719-2732, 2012. - 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. - 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. - X. B. Gao and L.-Z. Liao,
*Stability and convergence analysis for a class of neural networks*, IEEE TNN, 22 (11), 1770-1782, 2011. - 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. - 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. - 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. - 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. - 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. - X. Wang, B. S. He, and L.-Z. Liao,
*Steplengths in the extragradient type methods*, JCAM, 233 (11), 2925-2939,2010. - M. Li, L.-Z. Liao, and X. M. Yuan,
*Proximal point algorithms for general variational inequalities*, JOTA, 142 (1), 125-145, 2009. - X. B. Gao and L.-Z. Liao,
*A new projection-based neural network for constrained variational inequalities*, IEEE TNN, 20 (3), 373-388, 2009. - 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. - B. S. He, M. Li, and L.-Z. Liao,
*An improved contraction method for structured monotone variational inequalities*, Optimization, 57 (5), 643-653, 2008. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - G. H. Golub and L.-Z. Liao,
*Continuous methods for extreme and interior eigenvalue problems*, LAA, Vol. 415, pp. 31-51, 2006. - 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. - 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. - 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. - L.-Z. Liao,
*A continuous method for convex programming problems,*, JOTA, 124 (1): 207-226, 2005. - 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. - 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. - L.-Z. Liao, H. D. Qi, and L. Q. Qi,
*Neurodynamical optimization*, Journal of Global Optimization, 28, pp. 175-195, 2004. - 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. - 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 - B. S. He, L.-Z. Liao, and Z. H. Yang
*A new approximate proximal point algorithm for maximal monotone operator*, Science in China, Series A, 46 (2), pp. 200-206, 2003. - 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. - 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. - L.-Z. Liao and D. Li,
*Adaptive differential dynamic programming for multiobjective optimal control*, Automatica, 38 (6), pp. 1003-1015, 2002. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - L.-Z. Liao,
*A recurrent neural network for N-stage optimal control problems*, Neural Processing Letters, 10 (3), pp. 195-200, 1999. - L.-Z. Liao and H. Qi,
*A neural network for the linear complementarity problem*, Mathl. Comput. Modelling, 29 (3), pp. 9-18, 1999. - 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. - 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.