Abstract: In this paper, a new ODE-based hybrid 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. If the trial step cannot be accepted, a modified Wolfe-type nonmonotone line search is performed to generate a new iterative point, thus avoiding resolving the linear equation system. Under some assumptions, the algorithm is proven to be globally and locally convergent. Numerical results are also reported that show the efficiency of this proposed method.

Key words: unconstrained optimization, nonmonotone line search, trust region technique, IMPBOT algorithm, convergence