A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems (Journal of Computational Mathematics, 2018)
Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio $ρ_k$ for evaluating the trial step $d_k$ whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.
Keywords: Unconstrained optimization problems; nonmonotone trust region method; global convergence; superlinear convergence.