The divergence of the BFGS and Gauss Newton Methods

Abstract

We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the examples published recently in this journal, like unit steps and convexity along the search lines. As these other examples, the iterates, function values and gradients in the new examples fit into the general formulation in our previous work {\it On the divergence of line search methods, Comput. Appl. Math. vol.26 no.1 (2007)}, which also presents an example of divergence for Newton's method.