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:*

```
cvx_begin
variable x(n);
dual variable y;
minimize( c' * x );
y : A * x <= b;
cvx_end
```

*[…]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?

Bests

Roberto