A nonmonotone trust region method for unconstrained optimization
The authors propose a combination of a nonmonotone technique, fixed step length and the trust region method, in order to minimize a twice continuously differentiable unconstrained function, in the aim to improve the algorithm of \textit{J. Nocedal} and \textit{Y. Yuan} [Appl. Optim. 14, 153--175 (1998; Zbl 0909.90243)] and make it more effective in practical implementation. The main difference between the proposed method and the original method is that in the former one a step length is computed by a line search when the trial step is not successful, whereas in the present method a step length is defined by a formula. It is proved under mild conditions that the algorithm is global and superlinear convergent. Some numerical test on known test problems with the original and the new proposed modification are provided.
scientific article; zbMATH DE number 5004362