Continuing the discussion from Getting duals for nonlinear programming problem:
As an extension, I asked ChatGPT this problem.
Can anyone tell me where is its idea from? Does its reply make sense?
It does not make sense. Ipopt cannot provide a global dual bound.
2 Likes
I agree.
Here are my thoughts:
If the primal problem is a Min problem, then the dual problem is a Max-Min problem.
A dual bound can typically be obtained at a dual feasible point (e.g. μ_0).
However, this entails an exact (i.e. global) Minimization subprocedure.
If this (simpler) subprocedure itself doesn’t admit a global solution, a valid dual bound can not be derived.