The time complexity of maximum matching by simulated annealing
Journal of the ACM (JACM)
Cooling schedules for optimal annealing
Mathematics of Operations Research
On the convergence rate of annealing processes
SIAM Journal on Control and Optimization
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
SIAM Journal on Computing
On the convergence of reversible Markov chains
SIAM Journal on Matrix Analysis and Applications
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
The metropolis algorithm for graph bisection
Discrete Applied Mathematics
On the Convergence and Applications of Generalized Simulated Annealing
SIAM Journal on Control and Optimization
An Extension of Path Coupling and Its Application to the Glauber Dynamics for Graph Colorings
SIAM Journal on Computing
Improved Bounds for Mixing Rates of Marked Chains and Multicommodity Flow
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Simulated annealing, acceleration techniques, and image restoration
IEEE Transactions on Image Processing
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We discuss the asymptotic behavior of time-inhomogeneous Metropolis chains for solving constrained sampling and optimization problems. In addition to the usual inverse temperature schedule (&bgr;n)n∈[hollow N]*, the type of Markov processes under consideration is controlled by a divergent sequence (θn)n∈[hollow N]* of parameters acting as Lagrange multipliers. The associated transition probability matrices (P&bgr;n,θn)n∈[hollow N]* are defined by P&bgr;,θ = q(x, y)exp(−&bgr;(Wθ(y) − Wθ(x))+) for all pairs (x, y) of distinct elements of a finite set &OHgr;, where q is an irreducible and reversible Markov kernel and the energy function Wθ is of the form Wθ = U + θV for some functions U,V : &OHgr; → [hollow R]. Our approach, which is based on a comparison of the distribution of the chain at time n with the invariant measure of P&bgr;n,θn, requires the computation of an upper bound for the second largest eigenvalue in absolute value of P&bgr;n,θn. We extend the geometric bounds derived by Ingrassia and we give new sufficient conditions on the control sequences for the algorithm to simulate a Gibbs distribution with energy U on the constrained set [&OHgr; with tilde above] = {x ∈ &OHgr; : V(x) = minz∈&OHgr; V(z)} and to minimize U over [&OHgr; with tilde above].