Asymptotic Global Behavior for Stochastic Approximation and Diffusions with Slowly Decreasing Noise Effects: Global Minimization via Monte Carlo

1987 ◽  
Vol 47 (1) ◽  
pp. 169-185 ◽  
Author(s):  
H. J. Kushner
Keyword(s):  
Monte Carlo ◽  
Stochastic Approximation ◽  
Global Behavior ◽  
Global Minimization ◽  
Noise Effects

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (04) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

A Monte Carlo approach to crystal structure determination from powder diffraction data

2003 ◽  
Vol 36 (2) ◽  
pp. 239-243 ◽  
Author(s):  
V. Brodski ◽  
R. Peschar ◽  
H. Schenk
Keyword(s):  
Crystal Structure ◽  
Monte Carlo ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Determination ◽  
Global Minimization ◽  
Powder Diffraction Data ◽  
Unknown Structure ◽  
Space Method

A new direct-space method forab initiosolution of crystal structures from powder diffraction data is presented. The approach consists of a combined global minimization ofRwpand the potential energy of the system. This method was tested on two organic compounds with known structure and also applied successfully in the structure determination of the previously unknown structure of melamine pyrophosphate.

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