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.

Keywords:

• Nonlinear programming
• unconstrained optimization
• trust region algorithm
• nonmonotonicity
• forgetting factor

2020 Mathematics Subject Classifications:

• 90C53
• 65K05
• 49M37

Acknowledgments

The authors thank the anonymous reviewers for their valuable suggestions that helped to improve the quality of this work.

Data Availability

The authors confirm that the data supporting the findings of this study are available within the manuscript. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).