Semismoothness of the maximum eigenvalue function of a symmetric tensor and its application
type: Item
instance of: scholarly article
title: Semismoothness of the maximum eigenvalue function of a symmetric tensor and its application
zbMATH Open document ID: 1260.15010
author: G. Li
author: Liqun Qi
author: Gaohang Yu
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: The authors have examine the maximum eigenvalue function of an even order real symmetric tensor, regarding continuity, convexity, and differentiality using variational techniques. A sufficient condition ensuring the strong semi-smoothness of the maximum eigenvalue function is also proven. Besides this, a generalized Newton method to solve the space tensor conic linear programming problem is proposed as an application.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 6125892
zbMATH Keywords: symmetric tensor
zbMATH Keywords: maximum eigenvalue function
zbMATH Keywords: real polynomial
zbMATH Keywords: semi-smooth
zbMATH Keywords: generalized Newton method
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
full work available at URL: j.laa.2011.10.043
OpenAlex ID: W2057944397
Wikidata QID: Q59241508
cites work: Q4513935
cites work: The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
cites work: Tame functions are semismooth
cites work: Q4503250
cites work: Perron-Frobenius theorem for nonnegative tensors
cites work: On eigenvalue problems of real symmetric tensors
cites work: Q4209232
cites work: Optimization and nonsmooth analysis
cites work: Finite-Dimensional Variational Inequalities and Complementarity Problems
cites work: Second Order Sufficient Conditions for Weak and Strict Constrained Minima
cites work: The Łojasiewicz exponent of an analytic function at an isolated zero
cites work: Q3141900
cites work: Generalized Newton's method based on graphical derivatives
cites work: On the best rank-1 approximation of higher-order supersymmetric tensors
cites work: Tensor Decompositions and Applications
cites work: On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
cites work: Nonsmooth analysis of eigenvalues
cites work: On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials
cites work: Global error bounds for piecewise convex polynomials
cites work: Error Bounds of Generalized D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems
cites work: Semismooth and Semiconvex Functions in Constrained Optimization
cites work: Finding the Largest Eigenvalue of a Nonnegative Tensor
cites work: An Eigenvalue Method for Testing Positive Definiteness of a Multivariate Form
cites work: Nonsmooth Equations: Motivation and Algorithms
cites work: Eigenvalues of a real supersymmetric tensor
cites work: A nonsmooth version of Newton's method
cites work: Multivariate polynomial minimization and its application in signal processing
cites work: Space tensor conic programming
cites work: Higher Order Positive Semidefinite Diffusion Tensor Imaging
cites work: Q4496287
cites work: Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems
DOI: 10.1016/J.LAA.2011.10.043
description: scientific article; zbMATH DE number 6125892