Nonmonotone trust region algorithm for unconstrained optimization problems
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.
scientific article; zbMATH DE number 5836723