A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

In this paper, we present a new relaxed nonmonotone trust region method with adaptive radius for solving unconstrained optimization problems. The proposed method combines a relaxed nonmonotone technique with a modified version of the adaptive trust region strategy proposed by Shi and Guo (J Comput Appl Math 213:509–520, 2008). Under some suitable and standard assumptions, we establish the global convergence property as well as the superlinear convergence rate for the new method. Numerical results on some test problems show the efficiency and effectiveness of the new proposed method in practice.