New non-monotone line search-based adaptive trust region for solving unconstrained optimization problems

This paper deals with the adaptive trust region method with non-monotone line search. We first present a new inexact non-monotone line search and then apply it to the adaptive trust region framework. This method uses the advantage of the line search and non-monotone technique to increase the probability of acceptance of the trial step. The new algorithm exploits an adaptive radius in each iteration that contains first- and second-order information. The properties of global convergence and local superlinearity of the new algorithm are established under standard conditions. Numerical experiments on a set of test functions show the effectiveness of the proposed algorithm.