Some Research About Nonmono-tone ODE-type Trust Region Method

This paper focuses on two kinds of different non-monotone techniques and gives two different non-monotone ODE-type trust region algorithm. In Algorithm1, we advance the traditional non-monotone techniques, which reduces the number of iterations and the number of solving trust region sub-problems. In Algorithm2, we combine the trust region technique with new non-monotone Wolf line search technique, making linear equations to be solved only once at each iteration, thus the speed of convergence is greatly improved. Under certain conditions, this paper also prove that the two algorithm's global convergence and local convergence. Numerical results show that the proposed algorithms are effective and feasible.