# Shenglong Hu

Shenglong Hu

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

You can find me through shenglonghu AT hdu one dot edu one dot cn

My research interests are mathematical optimization and numerical multilinear algebra.

Articles and Manuscripts

Manuscripts

(With Ke Ye) When geometry meets optimization theory: partially orthogonal tensors, arXiv: 2201.04824.

Selected Journal Papers

27. (With Ke Ye) Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations, Mathematical Programming, 2023, 199: 1305-1364. arXiv: 1912.04085.

26. (With Guoyin Li) B-subdifferentials of the projection onto the matrix simplex, Computational Optimization and Applications, 2021, 80: 915-941.

25. Certifying the global optimality of quartic minimization over the sphere, Journal of the Operations Research Society of China, 2022, 10: 241-287.

24. Nondegeneracy of eigenvectors and singular vector tuples of tensors, Science China Mathematics, 2022, 65: 2083-2092. arXiv: 2104.05900.

23. (With Defeng Sun and Kim-Chuan Toh) Best nonnegative rank-one approximations of tensors, SIAM Journal on Matrix Analysis and Applications, 2019, 40: 1527-1554. arXiv: 1810.13372.

22. An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors, Computational Optimization and Applications, 2020, 75: 701-737.

21. Symmetry of eigenvalues of Sylvester matrices and tensors, Science China Mathematics, 2020, 63: 845-872.

20. (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.

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

18. (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.

17. (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.

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

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

14. (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.

13. (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.

12. (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.

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.

10. (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.

9. (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.

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

7. (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.

6. (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.

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

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

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

2. (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.

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

1. A note on the positive eigenvector of nonnegative tensors. July 2010.

2. (With Lieven De Lathauwer, Johan A.K. Suykens and Yuning Yang) Convergence study of block singular value maximization methods for rank-1 approximation to higher order tensors, 2016, ftp file.

Conferences and Workshops

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.

Nonnegative tensor partition, International Conference on Tensor, Matrix and Their Applications Spectral Theory of Tensors, May 20–May 24, 2016, Chern Institute of Mathematics, Nankai University, Tianjin, China.

Convergence study of BSVMM for rank one approximation to tensors, The 60th annual meeting of Australia Mathematical Society, December 5--8, 2016, The Australia National University, Canberra, Australia.

Spectral symmetry of a uniform hypergraph, The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), July 15-July 19, 2019, Valencia, Spain.

Education

Ph. D. in Applied Mathematics (2013), The Hong Kong Polytechnic University

B. S. in Mathematics (2008) and M. S. in Operations Research (2010), Tianjin University

Research Orbits

Research Associate of Prof. Liqun Qi, The Hong Kong Polytechnic University, April-May, July-August, 2013; June-August, 2016

Visiting Fellow of Prof. Yuan Yao, Peking University, March-April, 2014

Visiting Fellow, CAMP, National Institute for Mathematical Science, Korea, May-August, 2014

Research Fellow of Prof. Defeng Sun and Prof. Kim Chuan Toh, National University of Singapore, September, 2014-September, 2015

Postdoctoral Scholar of Prof. Lek-Heng Lim in department of statistics, The University of Chicago, October, 2015-March, 2016.

Visitor of Prof. Guoyin Li in department of applied mathematics, The University of New South Wales, November-December, 2016.

Associate Professor, Department of Mathematics, Tianjin University, April, 2014-April, 2018.

Professor, Department of Mathematics, School of Science, Hangzhou Dianzi University, April, 2018-present.

History

Outstanding Student from Sichuan Province, 2004

Student Science Award from Tianjin University, 2009

Research Award for Young Mathematicians from Tianjin Mathematical Society, 2017

Research Award for Low Rank Approximation on Tensors from Zhejiang Mathematical Society, 2021