A derivative-free algorithm for sparse unconstrained optimization problems

Benoit Colson, Philippe Toint

    Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter

    Abstract

    We consider the problem of minimizing a function whose derivatives are not available. This paper first presents an algorithm for solving problems of this class using interpolation polynomials and trust-region techniques. We then show how both the data structure and the procedure allowing to build the interpolating polynomials may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse with a general sparsity pattern. The favourable behaviour of the resulting algorithm is confirmed with numerical experiments illustrating the advantages of the method in terms of storage, speed and function evaluations, the latter criterion being particularly important in the framework of derivative-free optimization.
    Original languageEnglish
    Title of host publicationTrends in industrial and applied mathematics
    Subtitle of host publicationProceedings of the 1st International conference on industrial and applied mathematics of the Indian subcontinent
    EditorsA. H Siddiqi, M Kocvara
    Place of PublicationDordrecht
    PublisherKluwer Academic Publishers
    Pages131-147
    Number of pages17
    Volume72
    Publication statusPublished - 2002

    Keywords

    • interpolation models
    • sparsity
    • trust-region methods
    • derivative-free optimization

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