Convergence of simulated annealing using Foster-Lyapunov criteria

2001 ◽  
Vol 38 (04) ◽  
pp. 975-994 ◽  
Author(s):  
Christophe Andrieu ◽  
Laird A. Breyer ◽  
Arnaud Doucet
Keyword(s):  
Simulated Annealing ◽  
Markov Chains ◽  
State Spaces ◽  
Compact Spaces ◽  
Convergence Results

Simulated annealing is a popular and much studied method for maximizing functions on finite or compact spaces. For noncompact state spaces, the method is still sound, but convergence results are scarce. We show here how to prove convergence in such cases, for Markov chains satisfying suitable drift and minorization conditions.

Convergence of simulated annealing using Foster-Lyapunov criteria

2001 ◽  
Vol 38 (4) ◽  
pp. 975-994 ◽  
Author(s):  
Christophe Andrieu ◽  
Laird A. Breyer ◽  
Arnaud Doucet
Keyword(s):  
Simulated Annealing ◽  
Markov Chains ◽  
State Spaces ◽  
Compact Spaces ◽  
Convergence Results

Simulated annealing is a popular and much studied method for maximizing functions on finite or compact spaces. For noncompact state spaces, the method is still sound, but convergence results are scarce. We show here how to prove convergence in such cases, for Markov chains satisfying suitable drift and minorization conditions.

scholarly journals Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations

2008 ◽  
Vol 40 (2) ◽  
pp. 454-472 ◽  
Author(s):  
Ivan Gentil ◽  
Bruno Rémillard
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Selection Method ◽  
Systematic Sampling ◽  
Selection Methods ◽  
Convergence Properties ◽  
Main Motivation ◽  
Empirical Basis ◽  
Convergence Results ◽  
Selection For

While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to ‘systematic sampling’ in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.

An ergodic L 2-theorem for simulated annealing in bayesian image reconstruction

1990 ◽  
Vol 27 (04) ◽  
pp. 779-791 ◽  
Author(s):  
Gerhard Winkler
Keyword(s):  
Simulated Annealing ◽  
Image Reconstruction ◽  
Markov Chains ◽  
Bayesian Image Reconstruction ◽  
Stochastic Relaxation

An ergodic L 2-theorem for inhomogeneous Markov chains covering simulated annealing with or without constraints and stochastic relaxation with or without constraints arising in Bayesian image reconstruction is proved. The derivation is self-contained.

Monotone and associated Markov chains, with applications to reliability theory

1987 ◽  
Vol 24 (03) ◽  
pp. 679-695 ◽  
Author(s):  
Bo Henry Lindqvist
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Reliability Theory ◽  
State Spaces ◽  
Partially Ordered ◽  
Ordered State

We study monotone and associated Markov chains on finite partially ordered state spaces. Both discrete and continuous time, and both time-homogeneous and time-inhomogeneous chains are considered. The results are applied to binary and multistate reliability theory.

Conductance bounds on the L 2 convergence rate of Metropolis algorithms on unbounded state spaces

2004 ◽  
Vol 36 (01) ◽  
pp. 243-266
Author(s):  
Søren F. Jarner ◽  
Wai Kong Yuen
Keyword(s):  
Convergence Rate ◽  
Markov Chains ◽  
Spectral Gap ◽  
Unbounded Domains ◽  
Decomposition Theorem ◽  
Metropolis Algorithm ◽  
The State ◽  
Bounded Domains ◽  
Target Density ◽  
State Spaces

In this paper we derive bounds on the conductance and hence on the spectral gap of a Metropolis algorithm with a monotone, log-concave target density on an interval of ℝ. We show that the minimal conductance set has measure ½ and we use this characterization to bound the conductance in terms of the conductance of the algorithm restricted to a smaller domain. Whereas previous work on conductance has resulted in good bounds for Markov chains on bounded domains, this is the first conductance bound applicable to unbounded domains. We then show how this result can be combined with the state-decomposition theorem of Madras and Randall (2002) to bound the spectral gap of Metropolis algorithms with target distributions with monotone, log-concave tails on ℝ.

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