A limited memory steepest descent method

Roger Fletcher

    Research output: Contribution to journalArticlepeer-review

    54 Citations (Scopus)


    The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional 'long' vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method.
    Original languageEnglish
    Pages (from-to)413-436
    Number of pages24
    JournalMathematical Programming
    Issue number1-2
    Publication statusPublished - Oct 2012


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