I have a linear programming problem like this:
minimize $c^t X$ under the constraint that $AX \ge b$.
I will need to solve this linear programming problem online many times. I need it to be as fast as possible.
Only the $c$ vector will change each time. $A$ and $b$ stays the same.
So part of me feels that I should solve the constraint $AX \ge b$ once and for all (even if it takes a long time to find all the vertices of the polyhedron), and then have a much faster linear programming problem to solve.
But I'm not sure how to do this, or where to start. Any help hugely appreciated!