An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Abstract

Trust region method is a robust method for optimization problems. In this paper, we propose a novel adaptive nonmonotone technique based on trust region methods for solving unconstrained optimization. In order to accelerate the convergence of trust region methods, an adaptive trust region is generated according to the Hessian of the iterate point. Both the nonmonotone techniques and this adaptive strategies can improve the trust region methods in the sense of convergence. We prove that the proposed method is locally superlinear convergence under some standard assumptions. Numerical results show that the new method is effective and has a high speed of convergence in practice.