Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19010
Title: Eigenvalue analysis of constrained minimization problem for homogeneous polynomial
Authors: Song, Y
Qi, L 
Keywords: Constrained minimization
Pareto H-eigenvalue
Pareto Z-eigenvalue
Principal sub-tensor
Issue Date: 2015
Publisher: Springer
Source: Journal of global optimization, 2015 How to cite?
Journal: Journal of global optimization 
Abstract: In this paper, the concepts of Pareto H-eigenvalue and Pareto Z-eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a symmetric tensor has at least one Pareto H-eigenvalue (Pareto Z-eigenvalue). Furthermore, the minimum Pareto H-eigenvalue (or Pareto Z-eigenvalue) of a symmetric tensor is exactly equal to the minimum value of constrained minimization problem of homogeneous polynomial deduced by such a tensor, which gives an alternative methods for solving the minimum value of constrained minimization problem. In particular, a symmetric tensor (Formula presented.) is strictly copositive if and only if every Pareto H-eigenvalue (Z-eigenvalue) of (Formula presented.) is positive, and (Formula presented.) is copositive if and only if every Pareto H-eigenvalue (Z-eigenvalue) of (Formula presented.) is non-negative.
URI: http://hdl.handle.net/10397/19010
ISSN: 0925-5001
EISSN: 1573-2916
DOI: 10.1007/s10898-015-0343-y
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