An algorithm using quadratic interpolation for unconstrained derivative free optimization A. R. Conn and Ph. L. Toint Report 95/6 This paper explores the use of multivariate interpolation techniques in the context of methods for unconstrained optimization that do not require derivative of the objective function. A new algorithm is proposed that uses quadratic models in a trust region framework. The algorithm is constructed to require few evaluations of the objective function and is designed to be relatively insensitive to noise in the objective function values. Its performance is analyzed on a set of 20 examples, both with and without noise.