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.
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© 2012 Springer Science+Business Media, LLC
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Borkar, V.S., Ejov, V., Filar, J.A., Nguyen, G.T. (2012). Interior Point and Cross-Entropy Algorithms. In: Hamiltonian Cycle Problem and Markov Chains. International Series in Operations Research & Management Science, vol 171. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3232-6_8
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DOI: https://doi.org/10.1007/978-1-4614-3232-6_8
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3231-9
Online ISBN: 978-1-4614-3232-6
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