Adaptive optimization of the Monte-Carlo method
type: Item
instance of: scholarly article
title: Adaptive optimization of the Monte-Carlo method
zbMATH Open document ID: 0839.93082
author: A. N. Nakonechnyj
author: V. D. Shpak
published in: Cybernetics and Systems Analysis
publication date: 1995-05-17T00:00:00Z
review text: Let \(\zeta(u)\) be a random nonnegative function where \(u\in U\) is from a closed convex bounded subset in a finite-dimensional Euclidean space. Assume that the mean function \(m(u)= E(\zeta(u))\) is a continuously differentiable convex function. It is constructed a sequence of random vectors \(u^j\) with \(P\{\lim_{k\to \infty} {1\over k} \sum^k_{j= 1} (\zeta(u^j))= m^*\}= 1\), where \(m^*= \min\{m(u): u\in U\}\) and a bound rate of convergence in probability is proved.
Mathematics Subject Classification ID: 93E35
zbMATH DE Number: 746014
zbMATH Keywords: Monte Carlo simulation
zbMATH Keywords: stochastic optimization
zbMATH Keywords: adaptive strategy
reviewed by: Wilfried Grecksch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 746014