A derivative-free algorithm for sparse unconstrained optimization problems

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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

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Keywords

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

Cite this

Colson, B., & Toint, P. (2002). A derivative-free algorithm for sparse unconstrained optimization problems. In A. H. Siddiqi, & M. Kocvara (Eds.), Trends in industrial and applied mathematics: Proceedings of the 1st International conference on industrial and applied mathematics of the Indian subcontinent (Vol. 72, pp. 131-147). Dordrecht: Kluwer Academic Publishers.