Journal of Theoretical Probability

, Volume 5, Issue 2, pp 223–249 | Cite as

Singular perturbed Markov chains and exact behaviors of simulated annealing processes

  • Chii-Ruey Hwang
  • Shuenn-Jyi Sheu
Article

Abstract

We study asymptotic properties of discrete and continuous time generalized simulated annealing processesX(·) by considering a class of singular perturbed Markov chains which are closely related to the large deviation of perturbed diffusion processes. Convergence ofX(t) in probability to a setS0 of desired states, e.g., the set of global minima, and in distribution to a probability concentrated onS0 are studied. The corresponding two critical constants denoted byd and Λ withd≤Λ are given explicitly. When the cooling schedule is of the formc/logt, X(t) converges weakly forc>0. Whether the weak limit depends onX(0) or concentrates onS0 is determined by the relation betweenc, d, and Λ. Whenc>Λ, the expression for the rate of convergence for each state is also derived.

Key Words

Simulated annealing singular perturbed Markov chains large deviation 

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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Chii-Ruey Hwang
    • 1
  • Shuenn-Jyi Sheu
    • 1
  1. 1.Institute of MathematicsAcademia SinicaTaipeiTaiwan, Republic of China

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