An ODE-based Hybrid Method Based On The Nonmonotone Technique

In this paper, a new ODE-based method is proposed for solving unconstrained optimization problems, which combines the idea of IMPBOT algorithm with the nonmonotone line search technique. A main feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step,thus avoiding resolving the trust region subproblem and reducing the amount of calculation. Then a modified Armijo-type nonmonotone line search is performed to generate a new iterative point instead of resolving the linear equation system. Under some reasonable assumptions, the algorithm is proven to be globally and locally convergent. Numerical results are also reported to show the efficiency of this proposed method.