From the literature on this subject, I can see that some author uses benchmarks with one variable and some others with more than one. I am trying to publish some work, but so far my benchmarks have been considered as unimpressive. Your answer will be very useful. Many thanks.
Indeed, this is such old territory that making contributions will be very hard indeed. What do you have in mind pursuing? The literature is filled with variations of Newton-like methods, including of course , limited-memory, quasi- and conjugate gradient variants that only use first-order information. To compare them all on a large, relatively unspecific test bed would be a waste, but if you have in mind a particular problem setting that puts a real challenge on Newton-like method would be another story.
I have started working on using hyper-heuristics to generate mathematical expression. Those should replace the derivatives, so f'(x) computer 0. It is a big gamble, but I think it could work.
Patricia
Let me know how it goes. And say hello to York from me - I was a visiting scholar 1993-94 and lived just outside of the city walls. :-)
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