How to transfer a max min problem with dualize function

[bmmddzgj]

I am dealing with two stage robust unit commitment in the following form


According to the well-known column and constraint generation algorithm, such model (6)-(24) can be divided into a master problem (25)-(28) and a subproblem. The subproblem is a max-min problem and can be transformed into a single level problem (29)-(38) by dual theory. Here's the transformed formulation.

I want to code with dualize function using yalmip. My problem is if I can apply dualize function to get the above subproblem. I want to keep the uncertainty parameter $u$ as a variable in it and add extra constraints (30)-(31) after getting the initial dual constraints (33)-(38).

By the way, I have tried to write the subproblem but ended in getting an unbounded tips.

[johanlofberg]

Most likely you are not supposed to use dualize, it does something very esoteric (it interprets a model in primal vs dual space)

[bmmddzgj]

Thank you. I still wanna ask if I can leverage robust optimization to handle the second level problem (16)-(24) with given $\mathcal{X}$ by yalmip.

[johanlofberg]

To complicated to see in all the details. YALMIP can compute z in {minimize c'*z subject to Az+By<=b for all y in Y} where Y is polytopic, and the "can solve" in practice depends on the complexity of Y and its consequences on deriving the robust counterpart, i.e a problem where y and the for-all operator are eliminated