edoc-Server der Humboldt-Universität zu Berlin

SPEPS Preprint

Author(s): Alexander Shapiro, Georgia Institute of Technology, Atlanta; Ohio State University
Tito Homem-de-Mello, Georgia Institute of Technology, Atlanta; Ohio State University
Title: On Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs
Date of Acceptance: 18.10.1999
Submission Date: 12.10.1999
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): Monte Carlo simulation, Two-stage stochastic programming with recourse, Large Deviations theory, convex analysis
Appeared in: SIAM Journal on Optimization 1.2000 (Vol. 11)
Society for Industrial and Applied Mathematics - SIAM (Philadelphia, Pa.)
Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex  

Abstract (eng):
In this paper we discuss Monte Carlo simulation based approximations of a stochastic programming problem. We show that if the corresponding random functions are convex piecewise smooth and the distribution is discrete, then (under mild additional assumptions) an opitmal solution of the approximating problem provides an exact optimal solution of the true problem with probability one for sufficiently large sample size. Moreover, by using theory of Large Deviations, we show that the probability of such an event approaches one exponentially fast with increase of the sample size. In particular, this happens in the case of two stage stochastic programming with recourse if the corresponding distributions are discrete. The obtained results suggest that, in such cases, Monte Carlo simulation based methods could be very efficient. We present some numerical examples to illustrate the involved ideas.
Access Statistics: These data concerning access statistics for individual documents have been compiled using the webserver log files aggregated by AWSTATS. They refer to a monthly access count to the full text documents as well as to the entry page.
 
As for format versions of a document which consist of multiple files (such as HTML) the highest monthly access number to one of the files (chapters) is shown respectivly.
 
To see the detailled access numbers please move the mouse pointer over the single bars of the digaram.
Startseite: 3 Zugriffe PDF: 3 Zugriffe Startseite: 2 Zugriffe PDF: 6 Zugriffe Startseite: 4 Zugriffe PDF: 9 Zugriffe Startseite: 2 Zugriffe PDF: 2 Zugriffe Startseite: 2 Zugriffe PDF: 1 Zugriffe PDF: 1 Zugriffe Startseite: 4 Zugriffe Startseite: 2 Zugriffe Startseite: 1 Zugriffe PDF: 3 Zugriffe Startseite: 2 Zugriffe Startseite: 1 Zugriffe PDF: 2 Zugriffe PDF: 2 Zugriffe PDF: 1 Zugriffe Startseite: 3 Zugriffe PDF: 7 Zugriffe Startseite: 1 Zugriffe PDF: 3 Zugriffe PDF: 3 Zugriffe PDF: 5 Zugriffe PDF: 8 Zugriffe PDF: 7 Zugriffe PDF: 3 Zugriffe Startseite: 1 Zugriffe PDF: 12 Zugriffe Startseite: 2 Zugriffe PDF: 4 Zugriffe Startseite: 1 Zugriffe PDF: 4 Zugriffe PDF: 3 Zugriffe Startseite: 2 Zugriffe PDF: 3 Zugriffe Startseite: 2 Zugriffe PDF: 1 Zugriffe Startseite: 3 Zugriffe PDF: 2 Zugriffe Startseite: 1 Zugriffe PDF: 3 Zugriffe PDF: 2 Zugriffe PDF: 6 Zugriffe Startseite: 1 Zugriffe PDF: 6 Zugriffe Startseite: 1 Zugriffe PDF: 4 Zugriffe Startseite: 1 Zugriffe PDF: 4 Zugriffe Startseite: 2 Zugriffe PDF: 2 Zugriffe Startseite: 1 Zugriffe PDF: 2 Zugriffe Startseite: 1 Zugriffe PDF: 4 Zugriffe Startseite: 1 Zugriffe PDF: 8 Zugriffe
Jul
11
Aug
11
Sep
11
Oct
11
Nov
11
Dec
11
Jan
12
Feb
12
Apr
12
May
12
Jun
12
Jul
12
Aug
12
Sep
12
Oct
12
Nov
12
Dec
12
Jan
13
Feb
13
Mar
13
Apr
13
May
13
Jun
13
Jul
13
Aug
13
Sep
13
Oct
13
Nov
13
Dec
13
Jan
14
Feb
14
Mar
14
Apr
14
May
14
Jun
14
Jul
14
Aug
14
Sep
14
Monat Jul
11
Aug
11
Sep
11
Oct
11
Nov
11
Dec
11
Jan
12
Feb
12
Apr
12
May
12
Jun
12
Jul
12
Aug
12
Sep
12
Oct
12
Nov
12
Jan
13
Feb
13
Mar
13
Apr
13
May
13
Jun
13
Jul
13
Aug
13
Sep
13
Oct
13
Nov
13
Dec
13
Jan
14
Feb
14
Mar
14
Apr
14
May
14
Jun
14
Jul
14
Aug
14
Sep
14
Startseite 3 2 4 2 2   4 2 1 2 1     3 1           1 2 1   2 2 3 1     1 1 1 2 1 1 1
PDF 3 6 9 2 1 1     3   2 2 1 7 3 3 5 8 7 3 12 4 4 3 3 1 2 3 2 6 6 4 4 2 2 4 8

Gesamtzahl der Zugriffe seit Jul 2011:

  • Startseite – 47 (1.24 pro Monat)
  • PDF – 136 (3.58 pro Monat)
 
 
Generated at 31.10.2014, 16:53:49