Originally posted by: lbr33

Suppose I have a LP as the one written as follows:

min c'x + h'y
s.t:

Af <= a

Bf + Dy <= b

Gf + Mx <= d

f in F

y in Y

x in X

If the set X is huge, I can generate the x variables dynamically, using column generation.

If the set F is also huge, can I also generate the f variables by column generation and find the same solution (as the case, in which only the x variables are generated dynamically)?

I am afraid that I cannot because if I don't have all the f variables in the Constraints Gf + Mx <= d, the dual variables associated with these Constraints won't have all the necessary information to find the new good x variables.
Has anyone ever seen a paper that does something like that?

Thank you