  Compressed sensing involves solving a minimization problem with objective
function $\Omega(\boldsymbol{x}) = \|\boldsymbol{x}\|_1$ and linear constraints
$\boldsymbol{A} \boldsymbol{x} = \boldsymbol{b}$. Previous work has explored
robustness to errors in $\boldsymbol{A}$ and $\boldsymbol{b}$ under special
assumptions. Motivated by these results, we explore robustness to errors in
$\boldsymbol{A}$ for a wider class of objective functions $\Omega$ and for a
more general setting, where the solution may not be unique. Similar results for
errors in $\boldsymbol{b}$ are known and easier to prove. More precisely, for a
seminorm $\Omega(\boldsymbol{x})$ with a polyhedral unit ball, we prove that
the set-valued map $S(\boldsymbol{A}) = \arg \min_{\boldsymbol{A}
\boldsymbol{x} = \boldsymbol{b}} \Omega(\boldsymbol{x})$ is calm in
$\boldsymbol{A}$, where calmness is a kind of local Lipschitz regularity.
