Authors

Citation

Hf. Chen et Bw. Schmeiser, Stochastic root finding via retrospective approximation, IIE TRANS, 33(3), 2001, pp. 259-275

Citations number

34

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Engineering Management /General

Journal title

IIE TRANSACTIONS

ISSN journal

0740-817X
→ ACNP

Volume

33

Issue

3

Year of publication

2001

Pages

259 - 275

Database

ISI

SICI code

0740-817X(200103)33:3<259:SRFVRA>2.0.ZU;2-2

Abstract

Given a user-provided Monte Carlo simulation procedure to estimate a functi
on at any specified point, the stochastic root-finding problem is to find t
he unique argument value to provide a specified function value. To solve su
ch problems, we introduce the family of Retrospective Approximation (RA) al
gorithms. RA solves, with decreasing error, a sequence of sample-path equat
ions that are based on increasing Monte Carlo sample sizes. Two variations
are developed: IRA, in which each sample-path equation is generated indepen
dently of the others, and DRA, in which each equation is obtained by append
ing new random variates to the previous equation. We prove that such algori
thms converge with probability one to the desired solution as the number of
iterations grows, discuss implementation issues to obtain good performance
in practice without tuning algorithm parameters, provide experimental resu
lts for an illustrative application, and argue that IRA dominates DRA in te
rms of the generalized mean squared error.