What is the benefit of using Manifold Optimization Approach (MOA)? I understand that it is more elegant and instead of dealing with constraints we redefine a space, a Manifold where the variable lives on the manifold so the classic optimization problem with constraints becomes an optimization problem without constraints in MOA. But in terms of result or (numerical) efficiency or convergence are there any remarkable differences?
If I can use both methodes why should I choose MOA over classical optimization with constraints? Or in what case shoud I choose MOA over classical optimization with constraints?