主要从事张量优化、连续优化理论与算法研究，建立了半无限凸规划交换法的收敛理论，提出了M-张量及多变形正定性判断的线性收敛和二阶收敛算法，建立了四元数张量SVD分解理论及彩色视频恢复的应用，建立了网络流量恢复问题的低秩优化模型，设计了快速算法，满足了工业通讯的实际应用要求。
主要论著：
1) Liang Chen, Ruoning Chen, Defeng Sun, Liping Zhang, Equivalent Characterizations of the Aubin Property for Nonlinear Semidefinite Programming, Math.Program. (2025), https://doi.org/10.1007/s10107-025-02231-2
2) Zhenzhi Qin, Zhenyu Ming, Defeng Sun, Liping Zhang, Low-rank quaternion tensor completion for color video inpainting via a novel factorization strategy, Math. Comp., (2025) 94： 2409-2456
3) Yongjun Chen, Liping Zhang, Dual Complex Adjoint Matrix and Applications to Hand-Eye Calibration and Multi-Agent Formation Control, Journal of Scientific Computing, (2025) 104:4
4) Yongjun Chen, Liping Zhang, Three-step Jacobi method for computing eigenvalues of dual quaternion Hermitian matrices, Computational and Applied Mathematics, (2025) 44:150
5) Yongjun Chen, Liping Zhang, Linear convergence of the Collatz method for computing the Perron eigenpair of primitive dual number matrix, Communication on Applied mathematics and Computation (2024), https://doi.org/10.1007/s42967-024-00426-6
6) Yan Li, Liping Zhang, A novel nonconvex relaxation approach to low-rank matrix completion of inexact observed data, SIAM Journal on Optimization, 2024(34), 2378-2410
7) Zhenyu Ming, Zhenzhi Qin, Liping Zhang, Yanwei Xu, Liqun Qi, Network traffic recovery from link-load measurements using tensor triple decomposition strategy for third-order traffic tensors, Journal of Computational and Applied Mathematics, 2024(447), 115901
8) Xingbang Cui, Liping Zhang, Computing the dominant eigenpair of an essentially nonnegative tensor via a homotopy method, Journal of Computational and Applied Mathematics, 2024(438), 115565
9) Wei Zhang, Zhenyu Ming, Liping Zhang, Yanwei Xu, A round trip time weighting model for one-way delay estimation, East Asian Journal on Applied Mathematics, 2024(14), 179-194
10) Xingbang Cui, Liping Zhang, A localized progressive hedging algorithm for solving nonmonotone stochastic variational inequalities, Mathematics of Operations Research, 2024(49), 1915-1937
11) Ruoning Chen, Liping Zhang, Zhenyu Ming, A parallel low rank matrix optimization method for recovering internet traffic network data via link flow measurement, Journal of Computational and Applied Mathematics, 2023(434) 115331
12) Xingbang Cui, Liping Zhang, On multistage pseudomonotone stochastic variational inequalities, Journal of Optimization Theory and Applications, 2023(199), 363-391
13) Liping Zhang, Defeng Sun, Zhenting Luan, Solvability of monotone tensor complementarity problems, Science China Mathematics, 2023(66), 647-664.
14) Yan Li, Liping Zhang, A smoothing Newton method preserving nonnegativity for solving tensor complementarity problems with $P_0$ mappings, Journal of Industrial and Management Optimization, 2023(19), 2251-2267
15) Zhenting Luan, Zhenyu Ming, Yuchi Wu, Wei Han, Xiang Chen, Bo Bai, Liping Zhang, Hankel tensor-based model and $l_1$-Tucker decomposition-based frequency recovery method for harmonic retrieval problem, Computational and Applied Mathematics, 2023(42), 14pages
16) Liping Zhang, Shouqiang Du, On Exchange methods for nonlinear semi-infinite programs, Asia-Pacific Journal of Operational Research, 2022(39), 2150043
17) Zhenting Luan, Yuchi Wu, Shangsuo Liang, Wei Han, Bo Bai, Liping Zhang, Modulation for massive unsourced random access based on tensor block term decomposition, IEEE Globecom Workshops (GC Wkshps) 2022, 637-643
18) Zhenyu Ming, Haoran Pang, Yanwei Xu, Liping Zhang, Wei Zhang, Estimating clock skew with one-way timestamps, IEEE Communication Letters, 2022(26), 2591-2595
19) Zhenyu Ming, Liping Zhang, Hao Wu, Yanwei Xu, M Bakshi, Bo Bai, Gong Zhang, An accurate and practical algorithm for internet traffic recovery problem, Neurocomputing 2022(467), 203-213
20) Zhenzhi Qin, Zhenyu Ming, Liping Zhang, Singular value decomposition of third order quaternion tensors, Applied Mathematics Letters, 2022(123), 107597
21) Liping Zhang, Chiyu Chen, A Newton-type algorithm for the tensor eigenvalue complementarity problem and some applications, Mathematics of Computation, 2021(90), 215-231
22) Zhenyu Ming, Liping Zhang, Yanwei Xu, M Bakshi, An algorithm for matrix recovery of high-loss-rate network traffic data, Applied Mathematics Modelling, 2021(96), 645-656
23) Xingbang Cui, Liping Zhang, Stochastic matrix linear complementarity problems: the Fischer-Burmeister function-based expected residual minimization, Computational and Applied Mathematics, 2021(40), 183
24) Haoran Zhu, Liping Zhang, An alternating direction method of multipliers for tensor complementarity problems, Computational and Applied Mathematics 2021(40), 14 pages
25) Ya Li, Shouqiang Du, Liping Zhang, Tensor quadratic eigenvalue complementarity problem, Pacific Journal of Optimization}, 2021(17), 251-268
26) Zhenzhi Qin, Liping Zhang, A new penalized least absolute deviation model for high dimensional sparse linear regression and an efficient sequential linear programming algorithm, Pacific Journal of Optimization, 2021(17), 227-250
27) Zhenyu Ming, Liping Zhang, Liqun Qi, Expected residual minimization method for monotone stochastic tensor complementarity problem, Computational Optimization and Applications, 2020(77), 871-896
28) Junjie Yue, Liping Zhang, Computing all Laplacian H-eigenvalues for a uniform loose path of length three, Computational and Applied Mathematics, 2020(39), 121-135
29) Junjie Yue, Liping Zhang, Finding all H-eigenvalues of signless Laplacian tensor for a uniform loose path of length three,Asia-Pacific Journal of Operational Research, 2020(37), 204007 (13pages)
30) Zhenting Luan, Liping Zhang, A new programmable iterative algorithm for identifying strong H-tensors, Computational and Applied Mathematics, 2019(38), 43-56
31) Chiyu Chen, Liping Zhang, Finding Nash equilibrium for a class of multi-person noncooperative games via solving tensor complementarity problem, Applied Numerical Mathematics, 2019(145), 456-468
32) Shouqiang Du, Liping Zhang, A mixed integer programming approach to the tensor complementarity problem, Journal of Global Optimization, 2019(73), 789-800
33) Zhenyu Ming, Liping Zhang, Yannan Chen, An irreducible polynomial functional basis of two-dimensional Eshelby tensors, Applied Mathematics and Mechanics, 2019(40), 1169-1180
34) Shouqiang Du, Liping Zhang, Chiyu Chen, Liqun Qi, Tensor absolute value equations, Science China Mathematics, 2018(61), 1695-1710
35) Junjie Yue, Liping Zhang, Mei Lu, Liqun Qi, The Adjacency and Signless Laplacian Spectra of Cored Hypergraphs and Power Hypergraphs, Journal of the Operations Research Society of China, 2017(5), 27-43
36) Shunsuke Hayashi, Soon-Yi Wu, Liping Zhang, Computation algorithm for convex semi-infinite program with second-order cones: special analyses for affine and quadratic case, Journal of Scientific Computing, 2016(68), 573-595
37) Junjie Yue, Liping Zhang, Mei Lu, Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths, Frontiers of Mathematics in China, 2016(11), 623-645.
38) Liping Zhang, Soon-Yi Wu, An efficient algorithm for min-max convex semi-infinite programming problems, Numerical Functional Analysis and Optimization, 2016(37), 1037-1059
39) Liping Zhang, Liqun Qi, Guanglu Zhou, M-tensors and some applications, SIAM Journal on Matrix Analysis and Applications, 2014(35), 437-452.
40) Liping Zhang, Liqun Qi, Yi Xu, Ziyan Luo, The dominant eigenvalue of an essentially nonnegative tensor, Numerical Linear Algebra with Applications, 2013(20), 929-941.
41) Liping Zhang, Linear convergence of an algorithm for largest singular value of a nonnegative rectangular tensor, Frontiers of Mathematics in China, 2013(8), 141-153.
42) Liping Zhang, Shu-Cherng Fang, Soon-Yi Wu, An entropy based central cutting plane algorithm for convex min-max semi-infinite programming problems, Science China Mathematics, 56(2013), 201-211
43) Liping Zhang, A Newton-type algorithm for solving problems of search theory, Advance in Operations Research, 2013(1), 513918
44) Liping Zhang, Liqun Qi, Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor, Numerical Linear Algebra with Applications, 2012(19),830-841.
45) Liping Zhang, Yuan Zhou, A new approach to supply chain network equilibrium models, Computers and Industrial Engineering, 2012(63), 82-88.
46) Liping Zhang, Liqun Qi, Yi Xu, Linear convergence of the LZI algorithm for weakly positive tensors, Journal of Computational Mathematics, 2012(30), 24-33.
47) Liping Zhang, Soon-Yi Wu, A new approach to the weighted peak-constrained least-square error FIR digital filter optimal design problem, Computation Optimization and Applications, 2011(50), 445-461.
48) Liping Zhang, Soon-Yi Wu, Marco A. Lopez, A new exchange method for convex semi-infinite programming, SIAM Journal on Optimization, 2010(20), 2959-2977.
49) Liping Zhang, Soon-Yi Wu, Robust solution to Euclidean facility location problems with uncertain data, Journal of Industrial and Management Optimization, 2010(6), 751-760
50) Liping Zhang, Soon-Yi Wu, An algorithm based on the generalized D-gap function for equilibrium problems, Journal of Computational and Applied Mathematics, 2009(231), 403-411.
51) Liping Zhang, Soon-Yi Wu, Tingran Gao, Improved smoothing Newton methods for $P_0$ nonlinear complementarity problems, Applied Mathematics and Computation, 2009(215), 324-332
52) Liping Zhang, Jiye Han, Unconstrained optimization reformulations of equilibrium problems, Acta Mathematics Sinica, 2009(25), 343-354.
53) Liping Zhang, Solvability of semidefinite complementarity problems, Applied Mathematics and Computation, 2008(196), 86-93.
54) Liping Zhang, A Nonlinear Complementarity Model for Supply Chain Network Equilibrium, Journal of Industrial and Management Optimization, 2007(3), 727-737.
55) Liping Zhang, A new trust region algorithm for nonsmooth convex minimization, Applied Mathematics and Computation, 2007(193), 135-142.
56) Liping Zhang, Jiye Han, Zhenghai Huang, Superlinear/Quadratic one-step smoothing Newton method for $P_0$-NCP, Acta Mathematica Sinica, 2005(21), 17-128.
57) Zhenghai Huang, Liping Zhang, Jiye Han, A hybrid smoothing-nonsmooth Newton-type algorithm yielding an exact solution of the $P_0$-LCP, Journal of Computational Mathematics, 2004(22), 797-806.
58) Liping Zhang, Xiangsun Zhang, Global linear and quadratic one-step smoothing Newton method for $P_0$-LCP, Journal of Global Optimization, 2003(25), 363-376
59) Dachuan Xu, Jiye Han, Zhenghai Huang, Liping Zhang, Improved approximation algorithms for max n/2-directed-bisection and max n/2-dense-subgraph, Journal of Global Optimization, 2003(27), 399-410.
60) Liping Zhang, On the convergence of a modified algorithm for the spherical facility location problem, Operations Research Letters, 2003(31), 161-166.
61) Liping Zhang, Ziyou Gao, Superlinear/quadratic one-step smoothing Newton method for $P_0$-NCP without strict complementarity, Mathematical Methods of Operations Research, 2002(56), 231-241.
62) Liping Zhang, A characterization of the Drazin inverse, Linear Algebra and its Applications, 335(2001), 183-188
63) Zhenghai Huang, Jiye Han, Dachuan Xu, Liping Zhang, The non-interior continuation methods for solving the $P_0$ function nonlinear complementarity problem, Science China Mathematics, 2001(44), 1107-1114.
64) Liping Zhang, Jiye Han, Dachuan Xu, Existence theorems of solution to variational inequality problems, Science China Mathematics, 2001(44), 212-219.
