I am a bit confused by the documentation on dual variables (section 4.7, page 24 in the pdf). It says:
To associate the dual variable y with the inequality constraint Ax⪯bin this LP, we use the following syntax:
dual variable y;
minimize( c' * x );
y : A * x <= b;
[…]In the unbounded case, x will contain an unbounded direction; i.e. , a point x satisfying
(1) c' * x = -1, A * x <= 0
[…]. In the infeasible case, […] y contains an unbounded dual direction; i.e., a point y satisfying
(2) b' * y = −1, A' * y = 0, y >= 0.
But what about mutiple constraints:
y: A * x <= b;
z: C * x <= d;
From what I understand if the primal is unbounded then for all constraints (1) should hold. While if the dual is unbounded then there exist a constraint for which (2) holds. Is this correct?