A nonmonotone adaptive trust region technique with a forgetting factor

Abstract

Nonmonotonicity has been considered to be essentially influential on the efficiency of the iterative procedures of nonlinear optimization. A review of the literature shows that the objective function values available from recent iterations provide worthier information in the nonmonotone schemes. So, with the aim of enhancing probability of applying more recent available function values, a nonmonotone trust region ratio is suggested using a forgetting factor. Meanwhile, modification of a recent adaptive formula for the trust region radius is devised by a nonmonotone reflection as well. Then, based on the two mentioned modifications, an adaptive nonmonotone trust region algorithm is given. In addition, convergence of the method is analysed under classic assumptions. To provide support for our theoretical arguments, computational merits of the given algorithm on a set of CUTEr test functions are depicted.