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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Vydané v:Journal of inequalities and applications Ročník 2011; číslo 1; s. 1 - 13
Hlavní autori: Lu, Nan, Zhang, Ying
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.01.2011
Springer Nature B.V
SpringerOpen
Predmet:
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
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Abstract 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.
AbstractList Abstract 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.
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.
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.[PUBLICATION ABSTRACT]
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.
ArticleNumber 4
Author Zhang, Ying
Lu, Nan
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10.1080/01630560903123304
10.1287/moor.1070.0300
10.1007/BF01390421
10.1016/j.cam.2007.08.024
10.1007/BF02896466
10.1007/BF01436488
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ContentType Journal Article
Copyright Lu and Zhang; licensee Springer. 2011. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Springer International Publishing AG 2011
Copyright_xml – notice: Lu and Zhang; licensee Springer. 2011. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Keywords smoothing-type algorithm
local quadratic convergence
Symmetric cone; Euclidean Jordan algebra
global convergence
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Snippet 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...
Abstract 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...
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SubjectTerms 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
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Title A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone
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