Constraints on objective

[lorenzosteccanella]

Hi,

I saw your amazing work on conditional gradients for training neural networks.
I have a non-linear problem that I was solving with Frank Wolf in the linear case and that I would like to extend to the neural network case, the problem is formulated as follow:

I saw your work but I don't have it clear if I can extend it to the case where the constraints are on the objective and not on the neural network weights. Can you give me some hints about this?

Thanks,

Lorenzo