Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/32601
Title: Z-eigenvalue methods for a global polynomial optimization problem
Authors: Qi, L 
Wang, F
Wang, Y
Keywords: Orthogonal transformation
Polynomial optimization
Supersymmetric tensor
Z-eigenvalue
Issue Date: 2009
Source: Mathematical programming, 2009, v. 118, no. 2, p. 301-316 How to cite?
Journal: Mathematical Programming 
Abstract: As a global polynomial optimization problem, the best rank-one approximation to higher order tensors has extensive engineering and statistical applications. Different from traditional optimization solution methods, in this paper, we propose some Z-eigenvalue methods for solving this problem. We first propose a direct Z-eigenvalue method for this problem when the dimension is two. In multidimensional case, by a conventional descent optimization method, we may find a local minimizer of this problem. Then, by using orthogonal transformations, we convert the underlying supersymmetric tensor to a pseudo-canonical form, which has the same E-eigenvalues and some zero entries. Based upon these, we propose a direct orthogonal transformation Z-eigenvalue method for this problem in the case of order three and dimension three. In the case of order three and higher dimension, we propose a heuristic orthogonal transformation Z-eigenvalue method by improving the local minimum with the lower-dimensional Z-eigenvalue methods, and a heuristic cross-hill Z-eigenvalue method by using the two-dimensional Z-eigenvalue method to find more local minimizers. Numerical experiments show that our methods are efficient and promising.
URI: http://hdl.handle.net/10397/32601
ISSN: 0025-5610
DOI: 10.1007/s10107-007-0193-6
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

71
Last Week
0
Last month
3
Citations as of Apr 22, 2017

WEB OF SCIENCETM
Citations

65
Last Week
2
Last month
2
Citations as of Apr 27, 2017

Page view(s)

36
Last Week
2
Last month
Checked on Apr 23, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.