Lyapunov-type least-squares problems over symmetric cones
type: Item
instance of: scholarly article
title: Lyapunov-type least-squares problems over symmetric cones
zbMATH Open document ID: 1260.65032
author: Ziyan Luo
author: Lingchen Kong
author: Naihua Xiu
published in: Linear Algebra and its Applications
publication date: 2012-11-09T00:00:00Z
review text: An exploration of the linear image of a symmetric cone under the Lyapunov operator as well as a characterization of necessary and\(\backslash\)or sufficient conditions for the solution existence and uniqueness of the Lyapunov-type least-squares problem over a symmetric cone are done. The paper is organized as follows: The first section is an introduction. Some basic concepts and properties on a Euclidean Jordan algebra and a symmetric cone are collected and developed, and several preliminaries on convex analysis are reviewed in Section 2. Some intrinsic features and properties of the cone \(L_a(K)\) are explored for some given \(a \in \mathcal{J}\) in the next section. Section 4 is devoted to the solvability and uniqueness of the Lyapunov-type least-squares problem over the symmetric cone. Some concluding remarks are drawn in Section 5.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 6104553
zbMATH Keywords: Lyapunov matrix equation
zbMATH Keywords: Lyapunov-type least-squares problem
zbMATH Keywords: symmetric cone
zbMATH Keywords: solvability
zbMATH Keywords: uniqueness
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: j.laa.2012.06.020
OpenAlex ID: W2021712350
cites work: Q4040931
cites work: Structured and simultaneous Lyapunov functions for system stability problems
cites work: Optimal sampled-data control systems
cites work: Q4474321
cites work: Low-Rank Solution of Lyapunov Equations
cites work: Optimal matrices describing linear systems.
cites work: Positive Semidefinite Matrices: Characterization via Conical Hulls and Least-Squares Solution of a Matrix Equation
cites work: Erratum and Addendum: Positive Semidefinite Matrices: Characterization via Conical Hulls and Least-Squares Solution of a Matrix Equation
cites work: Least-squares solution of \(F=PG\) over positive semidefinite symmetric \(P\)
cites work: Q4946551
cites work: Computing a nearest symmetric positive semidefinite matrix
cites work: Computing the nearest correlation matrix--a problem from finance
cites work: An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem
cites work: Q5638112
cites work: Closedness criteria for the image of a closed set by a inear operator
cites work: On the Closedness of the Linear Image of a Closed Convex Cone
cites work: Numerical Methods for Quasi‐Linear Elliptic Equations with Nonlinear Boundary Conditions
cites work: Some P-properties for linear transformations on Euclidean Jordan algebras
cites work: On real Jordan algebras
cites work: Q4321748
cites work: Equivalent conditions for Jacobian nonsingularity in linear symmetric cone programming
cites work: Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
cites work: Q4747150
cites work: Q4830373
cites work: Relating Homogeneous Cones and Positive Definite Cones via T-Algebras
cites work: Q3141900
cites work: Q5513583
cites work: Q4068897
cites work: Some inertia theorems in Euclidean Jordan algebras
cites work: Similarity and other spectral relations for symmetric cones
cites work: Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric Cones
cites work: Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones
DOI: 10.1016/J.LAA.2012.06.020
description: scientific article; zbMATH DE number 6104553