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Z-eigenvalue methods for a global polynomial optimization problem

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WOS被引频次:75
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成果类型:
期刊论文
作者:
Qi, Liqun;Wang, Fei;Wang, Yiju
通讯作者:
Qi, LQ
作者机构:
[Qi, Liqun] Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
[Wang, Fei] Department of Mathematics, Hunan City University, Yiyang, Hunan, China
[Wang, Yiju] School of Operations Research and Management Sciences, Qufu Normal University, Rizhao Shandong 276800, China
通讯机构:
[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.
语种:
英文
关键词:
Applications. - Canonical forms - Eigenvalue methods - Eigenvalues - Higher dimensions - Higher orders - Local minimizers - Local minimums - Multidimensional cases - Numerical experiments - Optimization methods - Optimization solutions - Orthogonal transformation - Polynomial optimization - Polynomial optimization problems - Supersymmetric tensor - Z-eigenvalue
期刊:
Mathematical Programming
ISSN:
0025-5610
年:
2009
卷:
118
期:
2
页码:
301-316
文献类别:
WOS:Article;EI:Journal article (JA)
所属学科:
ESI学科类别:计算机科学;WOS学科类别:Computer Science, Software Engineering;Mathematics, Applied;Operations Research & Management Science
入藏号:
WOS:000262316200005;EI:20090411867779
基金类别:
Natural Science Foundation of China [10771120]
机构署名:
本校为其他机构
院系归属:
理学院
摘要:
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.
参考文献:
Anderson B.D., Bose N.K. and Jury E.I. (1975). Output feedback stabilization and related problems-solutions via decision methods. AC20: 55–66
Bose N.K. and Kamat P.S. (1974). Algorithm for stability test of multidimensional filters. ASSP-22: 307–314
Bose N.K. and Modarressi A.R. (1976). General procedure for multivariable polynomial positivity with control applications. AC-21: 596–601
Bose N.K. and Newcomb R.W. (1974). Tellegon’s theorem and multivariable realizability theory. 36: 417–425
Calamai P.H. and Moré J.J. (1987). Projected gradient methods for linearly constrained problems. 39: 93–116

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