On memory gradient method with trust region for unconstrained optimization (Q2492798)

The authors propose an algorithm to find a minimizer of a continuously differentiable unconstrained function and design an implementable version of the method analyzing its global convergence under weak conditions. The method combines line search methods and trust region methods to generate the new iterate points and sufficiently uses the previous multi-step iterative informations constructing the new iterative point from the previous \(m\)-step and hence an \(m\)-step memory gradient technique. Numerical results on test functions are presented.