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 language | English |
|---|---|
| Title of host publication | Trends in industrial and applied mathematics |
| Subtitle of host publication | Proceedings of the 1st International conference on industrial and applied mathematics of the Indian subcontinent |
| Editors | A. H Siddiqi, M Kocvara |
| Place of Publication | Dordrecht |
| Publisher | Kluwer Academic Publishers |
| Pages | 131-147 |
| Number of pages | 17 |
| Volume | 72 |
| Publication status | Published - 2002 |
Fingerprint
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.