The global convergence of the BFGS method under a modified Yuan-Wei-Lu line search technique

Abstract

This paper is focused on improving global convergence of the modified BFGS algorithm with Yuan-Wei-Lu line search formula. This improvement has been achieved by presenting a different line search approach and it is proved that the BFGS method with this line search converges globally if the function to be minimized has Lipschitz continuous gradients. The performance of the suggested algorithm is investigated via mathematical analysis and a simulation study.