A modified BFGS method and its convergence

Ganzhou Wu, Haiyan Liang

School of Science, Guangdong University of Petrochemical Technology, Maoming 525000, Guangdong, China

In this paper, a new modified BFGS method for unconstrained optimization problems is presented. The algorithm preserves the convergence properties of the famous BFGS algorithm. The relation between the new algorithm and a self-scaling quasi-Newton algorithm is revealed. If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution. And under some additional conditions, the superlinear convergence is given. Finally, the experimental results show that the proposed algorithm performs very well, which indicate that the numerical performance of the new algorithm is somewhat like the self-scaling quasi-Newton algorithm.