On the convergence of derivative-free methods for unconstrained optimization

Abstract

The purpose of this paper is to examine a broad class of derivative-free trust-region methods for unconstrained optimization inspired by the proposals of \citebb{Powe94b} and to derive a general framework in which reasonable global convergence results can be obtained. The developments make extensive use of an interpolation error bound derived by Sauer and Xu (1995) in the context of multivariate polynomial interpolation.