An adaptive trust-region method without function evaluations

In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate stationary points. As a corollary, we establish a global convergence result. We also present numerical results on benchmark problems. In terms of the number of calls of the oracle, the proposed method compares favorably with trust-region methods that use evaluations of the objective function.