



Research 












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Selected Articles: A continuation method for tensor complementarity
problems, Journal of Optimization Theory and Applications, (https://link.springer.com/article/10.1007/s1095701814222),
180, 2019, pp. 949963. (with L. Chen, H. Yin, and L. Zhou) A homotopy method for computing the largest eigenvalue of
an irreducible nonnegative tensor, Journal of Computational and Applied
Mathematics, 355, 2019, pp. 174181. Preprint. https://www.sciencedirect.com/science/article/pii/S0377042719300172 (with L. Chen and L. Zhou) Linear homotopy method for computing generalized tensor eigenpairs, Frontiers of Mathematics in China,(https://link.springer.com/article/10.1007/s114640170662z)
2017. Preprint.
A homotopy
method for solving multilinear systems with Mtensors, Applied Mathematics
Letters, 69, 2017, pp.4954. (http://dx.doi.org/10.1016/j.aml.2017.01.019) Preprint.
(with L. Chen
and L. Zhou) Computing tensor eigenvalues via homotopy methods, SIAM Journal on Matrix Analysis and
Applications, 37(1), 2016, pp.290319. (http://dx.doi.org/10.1137/15M1010725) arXiv
preprint. (with J. Xu) Proof of Stenger's
conjecture on matrix $I^{(1)}$ of Sinc methods, Journal of Computational and Applied
Mathematics, Vol. 255, 2014, pp. 805811. (doi: 10.1016/j.cam.2013.07.001.) Preprint. (This paper has been awarded $300
monetary prize by Professor Frank Stenger for
proving his Sinc matrix conjecture.) (with
D. Bunker and S. Zhang) A proximal ANLS algorithm for nonnegative tensor factorization
with a periodic enhanced line search, Applications of Mathematics, 58(5),
2013, pp.493509.( doi:10.1007/s1049201300262.) Preprint.
An unconstrained
optimization approach for finding real eigenvalues of even order symmetric
tensors, Numerical Algebra, Control, and Optimization, Vol. 3, No. 3, 2013,
pp.583599.(doi:10.3934/naco.2013.3.583.) Preprint. (with
S. Friedland and S. Gaubert) PerronFrobenius
theorem for nonnegative multilinear forms and extensions, Linear Algebra and
its Applications, Vol. 438, No. 2, 2013, pp.738749.( doi:10.1016/j.laa.2011.02.042.) Preprint. (This paper has been selected
as one of the 10 Notable Papers from Linear Algebra and Its Applications
published over the last 50 years, Link.) (with F. Gao
and K. Schilling) On the rate of convergence of iterated exponentials,
Journal of Applied Mathematics and Computing, Vol. 39, 2012, pp.8996.doi:
10.1007/s1219001105112 (with F. Gao) Implementing the NelderMead
simplex algorithm with adaptive parameters, Computational Optimization and Applications,
Vol. 51, No.1, 2012, pp. 259277. doi: 10.1007/s1058901093293 ( Matlab code download: here ) (with M.
Neumann and U. Prasad) Alternating projected BarzilaiBorwein
methods for nonnegative matrix factorization, Electronic Transactions on
Numerical Analysis, Vol. 36, 20092010, pp. 5482. ( Matlab code download: here ) (with J. Han,
M. Neumann, U. Prasad) On the convergence of the Image Space Reconstruction
Algorithm, Operators and Matrices, Vol. 3, No. 1, 2009, pp. 4158. (with J.
Axtell, D. Hershkowitz, M. Neumann, N. Sze) Optimization
of the spectral radius of a product for nonnegative matrices, Linear Algebra
and its Applications, Vol. 430, Issues 56, 2009, pp. 14421451. (with M.
Neumann) Inner product spaces, orthogonal projection, least squares, and
singular value decomposition, in Handbook of Linear Algebra, (editor: L.
Hogben), CRC Press, 1^{st} ed., 2006; 2^{nd} ed., 2013. (with M. Chen
and M. Neumann) On single and double Soules
matrices, Linear Algebra and its Applications, Vol. 416, 2006, pp.88110. (with M.
Neumann) Effect of dimensionality on the NelderMead
simplex method, Optimization Methods and Software, Vol. 21, No. 1, 2006, pp.
116. (with M.
Catral, M. Neumann, and R. Plemmons) On reduced
rank nonnegative matrix factorization for symmetric nonnegative matrices,
Linear Algebra and its Applications, Vol. 393, 2004, pp.107126. (with G. Liu)
On the convergence of the UOBYQA method, Journal of Applied Mathematics and
Computing, Vol. 16, No. 12, 2004, pp.125142. (with M.
Neumann) Combining quasiNewton and Cauchy directions, International Journal
of Applied Mathematics, Vol. 12, No.2, 2003, pp.167191. (with M.
Neumann and J. Xu) On the roots of certain polynomials arising from the
analysis of the NelderMead simplex method, Linear
Algebra and its Applications, Vol. 363, 2003, pp.109124. (with G. Liu
and L. Jing) Convergence properties of the DFP algorithm for unconstrained
optimization, Optimization, Vol. 51, No. 2, 2002, pp.731758. (with G. Liu) A
study of the DennisWolkowicz method on convex
problems, Computational Optimization and Applications, Vol. 19, 2001,
pp.297317. (with G. Liu
and L. Jing) A nonmonotone Broyden method for
unconstrained optimization, Optimization Methods and Software, Vol. 15, No.
2, 2001, pp.153172. (with M.
Neumann and M. Tsatsomeros) Spectral radii of fixed Frobenius
norm perturbations of nonnegative matrices, SIAM Journal on Matrix Analysis
and Applications, Vol.21, No.1, 2000, pp.7992. (with G. Liu,
L. Jing, and D. Han) A class of nonmonotone conjugate gradient methods for
unconstrained optimization, Journal of Optimization Theory and Applications,
Vol.101, No.1, 1999, pp.127140. (with G. Liu)
Global analysis of the DennisWolkowicz
leastchange secant algorithm, SIAM Journal on Optimization, Vol.8, No.3,
1998, pp.813832. (with L. Elsner, I. Koltracht, M.
Neumann, and M. Zippin) On a polygon equality
problem, Journal of Mathematical Analysis and Applications, Vol.223, 1998,
pp.6775. (with D. Han)
Convergence analysis of the selfdual optimally conditioned SSVM method of
OrenSpedicato, Optimization, Vol.37, 1996,
pp.153169. (with G. Liu)
Global convergence of quasiNewton methods for unconstrained optimization,
Chinese Science Bulletin, No.7, 1996, pp.529533. 










