A PL homotopy continuation method with the use of an odd map for the artificial level

M. Kojima; S. Oishi; Y. Sumi; K. Horiuchi

doi:10.1007/BF02591752

A PL homotopy continuation method with the use of an odd map for the artificial level

M. Kojima^*, S. Oishi, Y. Sumi, K. Horiuchi

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.

Original language	English
Pages (from-to)	235-244
Number of pages	10
Journal	Mathematical Programming
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/BF02591752
Publication status	Published - 1985 Jun 1

Keywords

Continuation Method
Fixed Point Algorithms
Odd Maps
Piecewise Linear Approximation
Systems of Equations

ASJC Scopus subject areas

Software
Mathematics(all)

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10.1007/BF02591752

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abstract = "This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.",

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AU - Kojima, M.

AU - Oishi, S.

AU - Sumi, Y.

AU - Horiuchi, K.

PY - 1985/6/1

Y1 - 1985/6/1

N2 - This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.

AB - This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.

KW - Continuation Method

KW - Fixed Point Algorithms

KW - Odd Maps

KW - Piecewise Linear Approximation

KW - Systems of Equations

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JO - Mathematical Programming

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ER -

A PL homotopy continuation method with the use of an odd map for the artificial level

Abstract

Keywords

ASJC Scopus subject areas

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