A new nonmonotone adaptive retrospective trust region method for unconstrained optimization problems (Q896192)

This paper proposes a new method for resolving a nonlinear unconstrained optimization problem with a twice-differentiable objective profit function. The authors develop a non-monotone adaptive retrospective trust region method and thus prove the global convergence of the new algorithm with a super-linear rate of convergence. A monotone variant of the classical and retrospective ratios and new non-monotone ratios based on convex combinations of the monotone ones is introduced. The paper is improved finally by a numerical example to prove the efficiency and the effectiveness of the proposed theory.