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Simulated annealing with time-dependent energy function via Sobolev inequalities

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  • Löwe, Matthias

Abstract

We analyze the simulated annealing algorithm with an energy function Ut that depends on time. Assuming some regularity conditions on Ut (especially that Ut does not change too quickly in time), and choosing a logarithmic cooling schedule for the algorithm, we derive bounds on the Radon-Nikodym density of the distribution of the annealing algorithm at time t with respect to the invariant measure [pi]t at time t. Moreover, we estimate the entrance time of the algorithm into typical subsets V of the state space in terms of [pi]t(Vc).

Suggested Citation

  • Löwe, Matthias, 1996. "Simulated annealing with time-dependent energy function via Sobolev inequalities," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 221-233, November.
    • Handle: RePEc:eee:spapps:v:63:y:1996:i:2:p:221-233
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    References listed on IDEAS

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    1. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
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    Cited by:

    1. Robini, Marc C. & Reissman, Pierre-Jean, 2011. "On simulated annealing with temperature-dependent energy and temperature-dependent communication," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 915-920, August.

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