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

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)235-244
Number of pages10
JournalMathematical Programming
Volume31
Issue number2
DOIs
Publication statusPublished - 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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