I have a convex polytope given as half-space representation
$$ A x \leq b $$
with matrix $A \in R^{M \times N}$, vector $x \in R^{N}$, vector $b \in R^{M}$ and $M>N$.
My question is: How can I efficiently compute a minimal half-space representation (without computing the vertex-representation)?
In other words, I want to reformulate the above inequality without modifying the corresponding polytope in order to obtain
$$ A^{*} x \leq b^{*}$$
where $A^{*}$ and $b^{*}$ have the minimum number of required rows (less rows compared to the original $A$ and $b$).
Or, in other words, I want to get rid of halfplanes in $A$ that do not intersect with the polytope.