Shenglong Hu

I am a professor in department of mathematics, School of Science,__ __Hangzhou Dianzi University.

Articles and Manuscripts

**Manuscripts**

**Journal Papers**

43. Symmetry of eigenvalues of Sylvester matrices and tensors, Science China Mathematics, 2019, online.

42. An elementary proof for the exact relaxation for rank one moment matrices in multi-polynomial SOS relaxation, Minmax Theory and its Applications, 2019, 4: 329--339.

41. (With Zheng-Hai Huang and Jie Wang) An inexact augmented Lagrangian multiplier method for solving quadratic complementary problems: An adapted algorithmic framework combining specific resolution techniques, Journal of Computational and Applied Mathematics, 2019, 361: 64–78.

40. (With Zheng-Hai Huang and Jie Wang) Error bounds for the solution sets of quadratic complementarity problems. Journal of Optimization Theory and Applications, 2018, 179: 983--1000.

# 39. (With Guoyin Li) Convergence rate analysis for the higher order power method in best rank one approximations of tensors. Numerische Mathematik, 2018, 140: 993--1031.

37. (With Ke Ye) Inverse eigenvalue problem for tensors. Communications in Mathematical Sciences, 2017, 15: 1627--1649. arXiv:1511.05057.

36. (With Liqun Qi) A necessary and sufficient condition for existence of a positive Perron vector. SIAM Journal on Matrix Analysis and Applications, 2016, 37: 1747--1770. arXiv:1511.07759.

35. (With Liqun Qi and Guofeng Zhang) Computing the geometric measure of entanglement of multipartite pure states by means of non-negative tensor. Physical Review A, 2016, 93: 012304. Previous version: The geometric measure of entanglement of pure states with nonnegative amplitudes and the spectral theory of nonnegative tensors. arXiv:1203.3675.

34. (With Ke Ye) Multuplicities of tensor eigenvalues. Communications in Mathematical Sciences, 2016, 14(4): 1049--1071. arXiv:1412.2831.

33. (With Xin-He Miao and Jiantao Yang) A generalized Newton method for absolute value equations associated with circular cones. Applied Mathematics and Computation, 2015, 269: 155--168.

32. (With Ji-Ye Han, Zheng-Hai Huang and Lei Yang) An iterative algorithm for third-order tensor multi-rank minimization. Computational Optimization and Applications, 2016, 63(1): 169--202.

31. (With Liqun Qi, Yisheng Song and Guofeng Zhang) Geometric measure of entanglement of multipartite mixed states. International Journal of Software & Informatics. 2014, 8(3/4): 317--326. arXiv:1204.4317.

30. Relations of the nuclear norm of a tensor and its matrix flattenings. Linear Algebra and its Applications, 2015, 478: 188--199. arXiv:1412.2443.

29. (With Liqun Qi and Jinshan Xie) The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph. Linear Algebra and its Applications, 2015, 469: 1--27. arXiv:1304.1315.

28. (With Guoyin Li and Liqun Qi) A tensor analogy of Yuan's theorem of the alternative and polynomial optimization with sign structure. Journal of Optimization Theory and Applications, 2016, 168: 446--474. arXiv:1407.2348.

27. (With Hong-Yan Ni and Yong Wang) A family of generalized NCP-functions and a smoothing reformulation of D-eigenvalues. Pacific Journal of Optimization, 2014, 10: 613--629.

26. (With Liqun Qi) Convergence of a second order Markov chain. Applied Mathematics and Computation, 2014, 241: 183--192. arXiv:1307.6919.

25. (With Liqun Qi) The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Discrete Applied Mathematics, 2014, 169: 140--151. arXiv:1303.4048.

24. (With Liqun Qi and Jia-Yu Shao) Some new trace formulas of tensors with applications in spectral hypergraph theory. Linear and Multilinear Algebra, 2015, 63: 971--992. arXiv:1307.5690.

23. (With Liqun Qi and Jia-Yu Shao) Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues. Linear Algebra and its Applications, 2013, 430: 2980--2998. arXiv:1304:1315.

22. (With Liqun Qi) The E-eigenvectors of tensors. Linear and Multilinear Algebra, 2014, 62(10): 1388--1402. arXiv:1303.2840.

21. (With Zheng-Hai Huang and Liqun Qi) Strictly nonnegative tensors and nonnegative tensor partition. Science in China Series A: Mathematics, 2014, 57: 181--195. Previous version: Finding the spectral radius of a nonnegative tensor, arXiv:1111.2138. This article won the best paper award in 2017.

20. (With Zheng-Hai Huang and Liqun Qi) Finding the extreme Z-eigenvalues of tensors via a sequential SDPs method. Numerical Linear** **Algebra with Applications, 2013, 20: 972--984.

19. (With Guoyin Li, Liqun Qi and Yisheng Song) Finding the maximum eigenvalue of essentially nonnegative symmetric tensors via sum of squares programming. Journal of Optimization Theory and Applications, 2013, 158: 713--738.

18. (With Liqun Qi) The Laplacian of a uniform hypergraph. Journal of Combinatorial Optimization, 2015, 29: 331--366.

17. (With Zheng-Hai Huang, Chen Ling and Liqun Qi) On determinant and eigenvalue theory of tensors. Journal of Symbolic Computation, 2013, 50: 508--531. Previous version: E-determinants of tensors, arXiv:1109.0348.

16. (With Liqun Qi) E-characteristic polynomial of a tensor of dimension two. Applied Mathematics Letters*,* 2013, 26: 225–231.

15. (With Tie Ni) A note on quadratic convergence of a smoothing Newton algorithm for the LCP. Optimization Letters, 2013, 7(3): 519–531.

14. (With Zheng-Hai Huang, Hong-Yan Ni and Liqun Qi) Positive definiteness of Diffusion Kurtosis Imaging. Inverse Problems and Imaging, 2012, 6(1): 57–75.

13. (With Zheng-Hai Huang) Theorems of the alternative for inequality systems of real polynomials. Journal of Optimization Theory and Applications, 2012, 154(1): 1–16.

12. (With Liqun Qi) Algebraic connectivity of an even uniform hypergraph. Journal of Combinatorial Optimization, 2012, 24(4): 564–579.

11. (With Zheng-Hai Huang) A note on approximating quadratic programming with rank constraint. Optimization, 2012, 61(5): 525–534.

10. (With Zheng-Hai Huang) Alternating direction method for bi-quadratic programming. Journal of Global Optimization, 2011, 51(3): 429--446.

9. (With Zheng-Hai Huang and Qiong Zhang) A generalized Newton method for absolute value equations associated with second order cones. Journal of Computational and Applied Mathematics, 2011, 235: 1490--1501.

8. (With Zheng-Hai Huang and Li-Yong Lu) Properties of a family of merit functions and a merit function method for the NCP. Applied Mathematics, A Journal of Chinese Universities, 2010, 25: 379--390.

7.(With Zheng-Hai Huang) Polynomial time solvability of non-symmetric semidefinite programming. Operation Research Letters, 2010, 38: 358--360.

6. (With Zheng-Hai Huang) A note on absolute value equations. Optimization Letters, 2010, 4: 417--424.

5. (With Zheng-Hai Huang and Nan Lu) Smoothness of a generalized merit function for the second-order cone complementarity problem. Pacific Journal of Optimization, 2010, 6: 551--571.

4. (With Zheng-Hai Huang and Nan Lu) A non-monotone line search algorithm for unconstrained optimization. Journal of Scientific Computing, 2010, 42: 38--53.

3. (With Jein-Shan Chen and Zheng-Hai Huang) Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems. Journal of Computational and Applied Mathematics, 2009, 230: 69–82.

2. (With Zheng-Hai Huang and Ping Wang) A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems. Optimization Methods and Software. 2009, 24: 447–460.

1. (With Ji-Ye Han and Zheng-Hai Huang) Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search. Science in China Series A: Mathematics. 2009, 52(4): 1–16.

**Unpublished Reports**

Non-monotone line search algorithm for unconstrained optimization on October 26, 2008, The 2-nd Annual meeting of the Society of Tianjin Industrial and Applied Mathematics, Tianjin University of Commerce.

Finding the spectral radius of a nonnegative tensor on December 18, 2010, JRI WorkShop On Eigenvalues of Nonnegative Tensors, The Hong Kong Polytechnic University.

Eigenvalues of Tensors: preliminary concepts and applications (hypergraph and quantum entanglement) on May 23 and May 26, 2012, Seminar on Eigenvalues of Tensors, Tianjin Univeristy.

The geometric measure of entanglement of pure states with nonnegative amplitudes and the spectral theory of nonnegative tensors, International Conference on Spectral Theory of Tensors, May 30–June 2, 2012, Chern Institute of Mathematics, Nankai University, Tianjin, China.

E-Characteristic polynomials of tensors, RTG workshop on Tensors and their Geometry in High Dimensions, September 26—September 29, 2012, MSRI, University of California at Berkeley.

Tensor analogies of alternative theorems, Optimization and Algebraic Geometry, June 16--June 20, 2014, CAMP, National Institute for Mathematical Science, Daejeon, Korea.

Spectral symmetry of a uniform hypergraph, The 19th International Linear Algebra Society Conference, August 6-August 9, 2014, Seoul, Korea.

Tensors in Computer Science and Geometry, November 10--November 14, 2014, Simons Institute, University of California at Berkeley.

Symbolic and Numerical Methods for Tensors and Representation Theory, November 17--November 20, 2014, Simons Institute, University of California at Berkeley.

Tensors and hypermatrices: decompositions and eigenvectors. 4th SIAM student chapter @NUS symposium on applied and computational math, May 29, 2015, National University of Singapore.

Eigenvalues of tensors and a second order Markov chain. SIAM conference on applied linear algebra, October 26-30, 2015, Hyatt Regency Atlanta, Atlanta, Georgia, USA.