Finding global minima with a novel filled function for non-smooth unconstrained optimisation

Abstract

This article presents a novel filled function approach for finding a better minimiser of both non-smooth and smooth unconstrained global optimisations. Unlike any traditional filled function, in theory, the filled function proposed in this article does not assume that the objective function is coercive. Moreover, the proposed function contains only one parameter, which can be easily adjusted. In the algorithm section, an algorithm based on the proposed filled function is presented for unconstrained global optimisation in which the objective function is assumed to be coercive. A numerical test is also provided. The preliminary computational results show that the proposed filled function approach is promising.

Keywords:

• Non-smooth unconstrained global optimisation
• filled function
• Filled function approach
• global minimiser

Acknowledgement

The authors thank the anonymous reviewers and the Editor for their constructive remarks and valuable comments which greatly improved this article's quality. This article was partially supported by The NNSF of China under Grant No. 10971053.