An adaptive nonmonotone trust region method for unconstrained optimization problems based on a simple subproblem

Using a simple quadratic model in the trust region subproblem, a new adaptive nonmonotone trust region method is proposed for solving unconstrained optimization problems. In our method, based on a slight modification of the proposed approach in (J. Optim. Theory Appl. 158(2):626-635, 2013), a new scalar approximation of the Hessian at the current point is provided. Our new proposed method is equipped with a new adaptive rule for updating the radius and an appropriate nonmonotone technique. Under some suitable and standard assumptions, the local and global convergence properties of the new algorithm as well as its convergence rate are investigated. Finally, the practical performance of the new proposed algorithm is verified on some test problems and compared with some existing algorithms in the literature.