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Interior Point and Cross-Entropy Algorithms

In: Hamiltonian Cycle Problem and Markov Chains

Author

Listed:
  • Vivek S. Borkar

    (IIT, Powai)

  • Vladimir Ejov

    (Flinders University)

  • Jerzy A. Filar

    (Flinders University)

  • Giang T. Nguyen

    (Université libre de Bruxelles)

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.

Suggested Citation

  • Vivek S. Borkar & Vladimir Ejov & Jerzy A. Filar & Giang T. Nguyen, 2012. "Interior Point and Cross-Entropy Algorithms," International Series in Operations Research & Management Science, in: Hamiltonian Cycle Problem and Markov Chains, edition 127, chapter 0, pages 143-159, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-3232-6_8
    DOI: 10.1007/978-1-4614-3232-6_8
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