Exploiting band structure in unconstrained optimization without derivatives

Benoit Colson, Philippe Toint

    Research output: Contribution to journalArticlepeer-review


    This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.
    Original languageEnglish
    Pages (from-to)399-412
    Number of pages14
    JournalOptimization and Engineering
    Issue number2
    Publication statusPublished - 2001


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

    Cite this