On the behaviour of a combined extra-updating/self-scaling BFGS method

This paper attempts to combine the best features of certain extra-updating BFGS method and self-scaling BFGS method. It describes an algorithm similar to the BFGS method, except that extra self-scaling updates are employed at some iterations. The BFGS Hessian is scaled and updated a number of times, depending on the information of the first-order derivatives. The results of numerical tests on certain sets of standard problems are reported. It is shown that the new algorithm is very competitive with the BFGS method in several cases.