I have two variables $x$, and $y$. That are related by $Bx=y$. There is also a linear inequality constraint on $x$: $Ax \leq b$. Is it possible to write down the feasible set of $y$ as a linear inequality constraint? How would I do this? I also know that the columns of $A$ are linearly independent, but I don't have any such condition on $B$.

  • $\begingroup$ In your question, is $b = B$? $\endgroup$ – Ryan Shesler Jun 19 '19 at 1:42
  • $\begingroup$ No, sorry if it wasn't clear. $b$ is a vector and is just the rhs of the inequality on $x$. $B$ is a matrix that maps $x$ to $y$. $\endgroup$ – user187815 Jun 19 '19 at 1:55
  • $\begingroup$ Related: mathoverflow.net/questions/179282/… $\endgroup$ – Marcus Ritt Jun 19 '19 at 2:53