Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30399
Title: Semismoothness of the maximum eigenvalue function of a symmetric tensor and its application
Authors: Li, G
Qi, L 
Yu, G
Keywords: Generalized Newton method
Maximum eigenvalue function
Real polynomial
Semismooth
Symmetric tensor
Issue Date: 2013
Publisher: North-Holland
Source: Linear algebra and its applications, 2013, v. 438, no. 2, p. 813-833 How to cite?
Journal: Linear algebra and its applications 
Abstract: In this paper, we examine the maximum eigenvalue function of an even order real symmetric tensor. By using the variational analysis techniques, we first show that the maximum eigenvalue function is a continuous and convex function on the symmetric tensor space. In particular, we obtain the convex subdifferential formula for the maximum eigenvalue function. Next, for an mth-order n-dimensional symmetric tensor A, we show that the maximum eigenvalue function is always ρth-order semismooth at A for some rational number ρ>0. In the special case when the geometric multiplicity is one, we show that ρ can be set as 1(2m-1)n. Sufficient condition ensuring the strong semismoothness of the maximum eigenvalue function is also provided. As an application, we propose a generalized Newton method to solve the space tensor conic linear programming problem which arises in medical imaging area. Local convergence rate of this method is established by using the semismooth property of the maximum eigenvalue function.
URI: http://hdl.handle.net/10397/30399
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2011.10.043
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