Interior Point and Cross-Entropy Algorithms

Abstract

In this chapter, we brie y discuss two recent algorithms that exploit two modern trends in optimisation in the context of our stochastic embedding of the Hamiltonian cycle problem: the interior point method and the importance sampling method. In particular, the first algorithm searches in the interior of the convex domain of doubly stochastic matrices induced by a given graph, with the goal of converging to an extreme point corresponding to a permutation matrix that coincides with a Hamiltonian cycle.