# The divergence of the BFGS and Gauss Newton methods

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## 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 Mascarenhas (Comput Appl Math 26(1), 2007), which also presents an example of divergence for Newton’s method.

## Mathematics Subject Classification

49M37 90C30## Supplementary material

10107_2013_720_MOESM1_ESM.txt (29 kb)

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© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013