A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equatio...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2011; no. 1; pp. 1 - 13
Main Authors: Lu, Nan, Zhang, Ying
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.01.2011
Springer Nature B.V
SpringerOpen
Subjects:
Algebra
Algorithms
Analysis
Applications of Mathematics
Classifications
global convergence
Inequalities
local quadratic convergence
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Smoothing
smoothing-type algorithm
Symmetric cone; Euclidean Jordan algebra
smoothing-type algorithm
local quadratic convergence
Symmetric cone; Euclidean Jordan algebra
global convergence
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found. By means of the theory of Euclidean Jordan algebras, the algorithm is proved to be well defined, and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective. AMS subject classifications: 90C33, 65K10.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2011-4