Solvability of Newton equations in smoothing-type algorithms for the SOCCP

In this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solva...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 8; pp. 2270 - 2276
Main Authors: Lu, Nan, Huang, Zheng-Hai
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.02.2011
Elsevier
Subjects:
Algebra
Algorithms
Computation
Exact sciences and technology
Jacobi matrix method
Jacobian matrix
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematical models
Mathematics
Matrices
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Optimization
Sciences and techniques of general use
Second-order cone complementarity problem
Smoothing-type algorithm
Solvability of Newton equations
Solvability of Newton equations
90C26
Second-order cone complementarity problem
90C30
Smoothing-type algorithm
90C33
Second order equation
Transcendental equation
Smoothing methods
Optimization method
Invertibility
Jacobi matrix
Algorithm
Matrix function
Equation system
Non linear equation
Numerical analysis
Smoothing
Applied mathematics
Algebraic equation
Problem solving
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solvability of such a system of Newton equations is given. In addition, our results also show that the assumption that the Jacobian matrix of the function involved in the SOCCP is a P 0 -matrix is not enough for ensuring the solvability of such a system of Newton equations, which is different from the one of smoothing-type algorithms for solving many traditional optimization problems in ℜ n .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.10.025