On Eigenvalues and Annealing Rates
- 1 August 1988
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 13 (3) , 508-511
- https://doi.org/10.1287/moor.13.3.508
Abstract
We evaluate asymptotically the eigenvalues of transition rate matrices (Qijϵ)i,j=1n with Qijϵ ∼ exp(−(U(j) − U(i))+/ϵ) for some function U using Ventcel's graphic method. As a consequence, we can compare the “nearly optimal” annealing rate in (Gidas, B. 1985. Global optimization via the Langevin equation. Proc. 24th IEEE Conf. Decision and Control, Ft. Lauderdale, FL, December.) with the true optimal rate in (Hajek, B. Cooling schedules for optimal annealing. Preprint.). A necessary and sufficient condition is given for the coincidence of those rates.Keywords
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