Notes on: A Randomized Polynomial-Time Simplex Algorithm

Note: c is the objective function, A a matrix and b, c the column vectors. Simplex method finds a solution to such a problem. • The set of feasible points of our LP is a polyhedron P := {x|Ax ≤ b} If P is non-empty then we have a convex polyhedron, where vertices are defined by d constraints, there where they are tight: aix = bi and ai are the rows of matrix A. Recall that: • A polyhedron is a set S ⊂ R: S = {x ∈ R|Ax ≤ b} • A polytope is a bounded polyhedron.