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A Doped Derivative-Free Algorithm

Abstract We propose a new class of algorithms to solve unconstrained nonlinear optimization problems, building on the framework of derivative-free methods. In many real applications, namely those involving running heavy pieces of software to compute the objective function, the derivatives are available, but at a prohibitive cost, involving finite differences or automatic differentiation. This justifies the use of derivative-free methods. The idea proposed in this paper is to improve the speed of convergence of such methods by allowing the algorithm to evaluate the derivatives from time to time, in such a way that the time spent in this evaluation is compensated by the faster convergence. We illustrate the superiority of the proposed approach on standard test problems.