An adaptive nonmonotone trust region algorithm

Abstract

Based on an eigenvalue analysis conducted on the scaled memoryless quasi-Newton updating formulas BFGS and DFP, an adaptive choice for the trust region radius is proposed. Then, using a trust region ratio obtained from a nonmonotone line search strategy, an adaptive nonmonotone trust region algorithm is developed. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan–Moré performance profile. They show efficiency of the proposed algorithm.

Keywords:

• unconstrained optimization
• trust region method
• quasi-Newton update
• adaptive radius
• global convergence
• superlinear convergence

Mathematics Subject Classifications (2010):

• 65K05
• 90C53
• 49M37

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was in part supported by the grant 95849086 from Iran National Science Foundation (INSF), and in part by the Research Council of Semnan University. The authors thank the anonymous reviewers and the associate editor for their valuable comments and suggestions helped to improve the quality of this work.