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

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

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Homotopy Continuation Method
    Linear equations
    Global Convergence
    Nonlinear equations
    Odd
    System of Nonlinear Equations
    Piecewise Linear
    Homotopy
    Linear equation
    Cover
    Sufficient Conditions

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Software
    • Engineering(all)

    Cite this

    A PL homotopy continuation method with the use of an odd map for the artificial level. / Kojima, M.; Oishi, Shinichi; Sumi, Y.; Horiuchi, K.

    In: Mathematical Programming, Vol. 31, No. 2, 06.1985, p. 235-244.

    Research output: Contribution to journalArticle

    @article{7c444be3d72a44549be1a731aba2822d,
    title = "A PL homotopy continuation method with the use of an odd map for the artificial level",
    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.",
    keywords = "Continuation Method, Fixed Point Algorithms, Odd Maps, Piecewise Linear Approximation, Systems of Equations",
    author = "M. Kojima and Shinichi Oishi and Y. Sumi and K. Horiuchi",
    year = "1985",
    month = "6",
    doi = "10.1007/BF02591752",
    language = "English",
    volume = "31",
    pages = "235--244",
    journal = "Mathematical Programming",
    issn = "0025-5610",
    publisher = "Springer-Verlag GmbH and Co. KG",
    number = "2",

    }

    TY - JOUR

    T1 - A PL homotopy continuation method with the use of an odd map for the artificial level

    AU - Kojima, M.

    AU - Oishi, Shinichi

    AU - Sumi, Y.

    AU - Horiuchi, K.

    PY - 1985/6

    Y1 - 1985/6

    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

    UR - http://www.scopus.com/inward/record.url?scp=0022014146&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0022014146&partnerID=8YFLogxK

    U2 - 10.1007/BF02591752

    DO - 10.1007/BF02591752

    M3 - Article

    AN - SCOPUS:0022014146

    VL - 31

    SP - 235

    EP - 244

    JO - Mathematical Programming

    JF - Mathematical Programming

    SN - 0025-5610

    IS - 2

    ER -