Improving nonmonotone trust-region methods

The trust-region family are one of the most important algorithms for solving unconstrained nonlinear programming. It is well known that using of the nonmonotone strategy in this family can improve the likelihood of finding the global optimum and the numerical performance. The traditional nonmonotone strategy contains some disadvantages. In this paper, we introduce new nonmonotone trust-region algorithm by incorporating a new nonmonotone strategy into the general trust-region framework, while new nonmonotone strategy is a convex combination of the maximum function value of some prior successful iterations with current function value. Under some classical assumptions, it is proven that the new algorithm is global convergence. Preliminary numerical results are presented to confirm efficiency of our approach