Cubically convergent method for locating a nearby vertex in linear programming (Q911456)

Given a point sufficiently close to a nondegenerate basic feasible solution \(x^*\) of a linear program, we show how to generate a sequence \(\{p^ k\}\) that converges to the 0-1 vector \(sign(x^*)\) at a Q-cubic rate. This extremely fast convergence enables us to determine, with a high degree of certainty, which variables will be zero and which will be nonzero at optimality and then construct \(x^*\) from this information.