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