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On multi-dimensional annealing problems

Published online by Cambridge University Press:  24 October 2008

Terence Chan
Terence Chan
Affiliation:
Statistical Laboratory, University of Cambridge, Cambridge CB2 1SB
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Extract

In [1] Chan and Williams considered a one-dimensional diffusion of the form

where F is a strictly increasing continuous function with F(0) = 0 and ε is a decreasing deterministic function such that ε(0) is finite and ε(t) ↓ 0 as t↑ ∞, and gave necessary and sufficient conditions for Yt →0 a.s. as t→∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 177 - 184
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Chan, T. and Williams, D.. An excursion approach to an annealing problem. Math. Proc. Cambridge Philos. Soc. 105 (1989), 169–176.CrossRefGoogle Scholar
[2]Chiang, T.-S., Hwang, C.-R. and Sheu, S.-J.. Diffusion for global optimization in n. SIAM J. Control Optim. 25 (1987), 737–753.CrossRefGoogle Scholar
[3]Hajek, B.. A tutorial survey of theory and applications of simulated annealing. (Lecture presented at the IEEE Conference on Decision and Control, December 1985.)CrossRefGoogle Scholar
[4]Hajek, B.. Cooling schedules for optimal annealing. Math. Oper. Res. 13 (1988), 311–329.CrossRefGoogle Scholar