Incorporating non-monotone trust region algorithm with line search method for unconstrained optimization

This paper concerns an efficient trust region framework that exploits a new non-monotone line search method. The new algorithm avoids the sudden increase of the objective function values in the non-monotone trust region method. Instead of resolving the trust region subproblem whenever the trial step is rejected, the proposed algorithm employs an Armijo-type line search method in the direction of the rejected trial step to construct a new point. Global and superlinear properties are preserved under appropriate conditions. Comparative numerical experiments depict the efficiency and robustness of the new algorithm using the Dolan-More performance profiles.