I am trying to understand two-stage chance-constrained LP and reading a paper, which has a title "A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support". But my question is simple, about a dual problem of LP.
In (6) in this paper, a dual problem of LP problem is shown. The primal problem is
minimize 0
s.t. Tx+Wy>=b, nonnegative y
(x is considered as nonnegative 'constant' here.)
We can easily obtain the dual problem:
maximize u'(b-Tx) (' means transpose)
s.t. u'W<=0, nonnegative u (u is the dual variable associated with the inequality constraint.)
But in this paper, the dual problem includes one more constraint, u'e=1
(e is a vector, all elements are 1. Equivalent to 'sum of all elements of u is 1'.)
I don't understand the reason of this constraint.
In this paper, the only specific statement is that it is a process of obtaining an 'extreme point' optimal solution, so I guess the additional equality constraint is related to the extreme point. But I don't get it clearly.
Could anybody explain this clearly? I would very appreciate it.