Trust-region based methods for unconstrained global optimization

Abstract

Convexity is an essential characteristic in optimization. In reality, many optimization problems are not unimodal which make their feasible regions to be non-convex. These conditions lead to hard global optimization issues even in low dimension. In this study, two trusted-region based methods are developed to deal with such problems. The developed methods utilize interval technique to find regions where minimizers reside. These identified regions are convex with at least one local minimizer. The developed methods have been proven to satisfy descent property, global convergence and low time complexities. Some benchmark functions with diverse properties have been used in the simulation of the developed methods. The simulation results show that the methods can successfully identify all the global minimizers of the unconstrained non-convex benchmark functions. This study can be extended to solve constrained optimization problems for future work.