Transform Standard-Dual program to Canonical-Dual program Say I have the following Standard-Dual linear program:
$$max&lt;\vec b, \vec y&gt;$$
$$s.t.:A^Ty \le \vec c$$
$$\vec y \ge \vec 0$$
Is there a way to transform it to a Canonical-Dual and equivalent linear program, i.e., that of the following form:
$$max&lt;\vec b', \vec y'&gt;$$
$$s.t.:A'^Ty' \le \vec c'$$
$$\vec y' \in \mathbb R^n$$
Yes. For each variable $y_i$, just add the constraint $-y_i \leq 0$, and then you don't have to assume that $\vec{y} \geq 0$.