I haven't really kept myself up to date with research on the simplex algorithm for several years. I have taught linear programming, but it has not focused on the cutting edge of things.
I remember many years ago I went to a course on linear programming, where the teacher said something along the lines of "When applying the simplex algorithm, its frustrating that we can "see" the optimal vertex all the time (convex feasible set) but we have to travel all the way around the edge of the polyhedron to get there".
My question is "what ideas have been proposed to make "short cuts" through the polyhedron when using the simplex algorithm"?
I know this is what interior point algorithms do, but this is in the context of the simplex algorithm.