A new trust region method with adaptive radius for unconstrained optimization

Abstract

In this paper, we propose a new adaptive trust region method for unconstrained optimization problems. In the new method, we use the previous and the current iterative information and a new update rule to define the trust region radius at each iterate. The global and superlinear convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

Keywords:

• unconstrained optimization
• trust region method
• adaptive technique
• global convergence
• superlinear convergence

Mathematics Subject Classification :

• 65K05
• 90C30

Acknowledgements

The authors would like to thank the editor and the reviewers for their insightful and constructive comments, which helped to enrich the content and improve the presentation of this paper.