On the global convergence of trust region algorithms for unconstrained minimization

Many trust region algorithms for unconstrained minimization have excellent global convergence properties if their second derivative approximations are not too large 2]. We consider how large these approximations have to be, if they prevent convergence when the objective function is bounded below and continuously differentiable. Thus we obtain a useful convergence result in the case when there is a bound on the second derivative approximations that depends linearly on the iteration number.