Nonmonotone trust region algorithm for unconstrained optimization problems (Q618133)

The usual trust region methods generate a sequence of iterates such that the objective function value sequence is monotonically decreasing; hence, they accept the trial step if the objective function has decreased sufficiently. It is proven that trust region method has strong convergence property and is efficient for optimization problem. However, a lot of numerical experiments indicate that enforcing monotonicity of the objective function value sequence may considerably slow the rate of convergence when the iteration is trapped near a narrow curved valley. Recent researches indicate that it might be advantageous to allow the algorithm to generate a nonmonotone objective function value sequence. In this paper, the authors present a new, nonmonotone trust region algorithm for unconstrained optimization problems. This method combines the nonmonotone technique proposed by \textit{H. Zhang} and \textit{W. W. Hanger} [SIAM J. Optim. 14, No.~4, 1043--1056 (2004; Zbl 1073.90024)] with the trust region method proposed by \textit{P. L. Toint} [Math. Program. 77, No.~1 (A), 69--94 (1997; Zbl 0891.90153)]. The method is also independent on the choice of parameter. Under suitable assumptions, global and superlinear convergence results are proved. The numerical results show that the presented method is efficient.