Nonmonotone trust region methods with curvilinear path in unconstrained optimization (Q1195967)

The usual trust region method with curvilinear path for an unconstrained minimization problem is replaced by a nonmonotone one. Although in this algorithm the sequence of function values could be nonmonotone, convergence of the method under conditions similar to the usual trust region method is proved. The two methods are compared on numerical examples which show that the nonmonotone one can allow a considerable computational saving, especially for the problem with narrow curving valleys.