Skip to Main content Skip to Navigation
Journal articles

Fast simulated annealing in $\R^d$ and an application to maximum likelihood estimation

Abstract : Using classical simulated annealing to maximise a function $\psi$ defined on a subset of $\R^d$, the probability $\p(\psi(\theta_n)\leq \psi_{\max}-\epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $\theta_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $\psi_{\max}$ is the maximal value of $\psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replaced by a more heavy-tailed function, and the system is cooled faster. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.
Document type :
Journal articles
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00093403
Contributor : Sylvain Rubenthaler Connect in order to contact the contributor
Submitted on : Wednesday, September 13, 2006 - 2:24:20 PM
Last modification on : Saturday, June 25, 2022 - 10:57:34 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 12:55:38 AM

Identifiers

Collections

Citation

Sylvain Rubenthaler, Tobias Rydén, Magnus Wiktorsson. Fast simulated annealing in $\R^d$ and an application to maximum likelihood estimation. Stochastic Processes and their Applications, Elsevier, 2009, 119 (6), pp.1912-1931. ⟨10.1016/j.spa.2008.09.007⟩. ⟨hal-00093403⟩

Share

Metrics

Record views

229

Files downloads

144