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
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
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?