On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

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    Abstract

    A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.
    Original languageEnglish
    Pages (from-to)511-529
    Number of pages19
    JournalJournal of Optimization Theory and Applications.
    Volume23
    Issue number4
    DOIs
    Publication statusPublished - 1 Dec 1977

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