I'm interested in portfolio optimization and there's a lot of modelizations out there using duality theory. Since I didn't study that yet, I searched around the net to understand what it means and kind of did. But I still have one issue : what does duality theory gives us ?
I mean, from where I stand, here is how I see it : We have a "primal" optimization problem with some variables and some constraints, we then "build" a dual problem with new variables (each old constraint -> one new variable) and new contraints. Then, in order to find a solution for our original problem, we solve the second one, the dual one.
My question is : What characteristics does the dual problem have that makes it simpler or more useful to solve ? What's the differences between the primal problem and the dual one ?
Also, if anyone has a good reference for the course, that explains what's behind it and gives practical examples, I would very much like to have it !
Thank you all.