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.
|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|
|Number of pages||17|
|Publication status||Published - 2002|
- interpolation models
- trust-region methods
- derivative-free optimization
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.