Global convergence of trust-region algorithms for convex constrained minimization without derivatives

In this work we propose a trust-region algorithm for the problem of minimizing a function within a convex closed domain. We assume that the objective function is differentiable but no derivatives are available. The algorithm has a very simple structure and allows a great deal of freedom in the choice of the models. Under reasonable assumptions for derivative-free schemes, we prove global convergence for the algorithm, that is to say, that all accumulation points of the sequence generated by the algorithm are stationary.