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. © 2009 Elsevier B.V. All rights reserved.
Ou, Y., Zhou, Q., & Lin, H. (2009). An ODE-based trust region method for unconstrained optimization problems. Journal of Computational and Applied Mathematics, 232(2), 318–326. https://doi.org/10.1016/j.cam.2009.06.012