Asymptotic convergence results

Abstract

Essential to the convergence proof for the homogeneous algorithm is the fact that, under certain conditions, the stationary distribution of a homogeneous Markov chain exists. The stationary distribution is defined as the vector q whose i-th component is given by [FELL50]

$${q_i} = \mathop {\lim }\limits_{k \to \infty } \Pr \{ X(k) = i|X(0) = j\} ,$$

((3.1))

for an arbitrary j.

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1. Philips Research Laboratories, Eindhoven, The Netherlands

   Peter J. M. van Laarhoven & Emile H. L. Aarts

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1. Peter J. M. van Laarhoven
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2. Emile H. L. Aarts
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© 1987 Springer Science+Business Media Dordrecht

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van Laarhoven, P.J.M., Aarts, E.H.L. (1987). Asymptotic convergence results. In: Simulated Annealing: Theory and Applications. Mathematics and Its Applications, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7744-1_3

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• DOI: https://doi.org/10.1007/978-94-015-7744-1_3

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