An ODE-based trust region method for unconstrained optimization problems

In this paper, a new trust region algorithm is proposed for solving unconstrained optimization problems. This method can be regarded as a combination of trust region technique, fixed step-length and ODE-based methods. A feature of this proposed method is that at each iteration, only a system of linear equations is solved to obtain a trial step. Another is that when a trial step is not accepted, the method generates an iterative point whose step-length is defined by a formula. Under some standard assumptions, it is proven that the algorithm is globally convergent and locally superlinear convergent. Preliminary numerical results are reported.