# Dual methods in structure optimization

I am studying Structure Optimization, and the teacher took a few weeks to detail dual methods, but I don't get why it is useful.

From an optimization problem with n design variables and m active constraints, the dual methods introduce an equivalent dual problem with m variables. If I understand correctly, these methods would allow faster resolution if m is far less than n.

However, in structural analysis (this course is using FEM methods), I would expect to have one constraint per element, and only a few design variables. For instance, I think it is usual to have a large number of elements to mesh a piece, but productions methods may only allow a constant thickness in the piece, or other constraints may limit the number of actual design variables. Hence I would expect to have a much larger m than n.

Is something wrong with this?

Also, I tried to look for publications about dual methods in this field, but I found nothing related. Is there a paper I could read about this subject?

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I don't know about the specifics for structural analysis, but yes the reason that you do optimizations in dual spaces is because, in general, they can often be quite easy and/or much faster... –  daaxix Jan 6 '13 at 17:23