3 problems

For a linear program with dimension $n$, consider a descent path, meaning a sequence of pivots that decreases the objective function at each step. Linear descent-path conjecture. T…

Let $P$ be a polytope equipped with a linear function, and consider the paths followed by the simplex method on the graph of $P$, along which the linear function increases. Count t…

Let $P$ be a $(0,k)$-lattice polytope of dimension $d$, and let the monotone diameter of $P$ be the maximum, over pairs of vertices and compatible linear objective functions, of th…