Probability Distribution Problems Concerning Stochastic Programming Problems

2010 ◽  
pp. 195-221
Author(s):  
András Prékopa
Keyword(s):  
Probability Distribution ◽  
Stochastic Programming ◽  
Distribution Problems

scholarly journals Convergence Analysis of a Stochastic Progressive Hedging Algorithm for Stochastic Programming

2020 ◽  
Vol 8 (3) ◽  
pp. 656-667
Author(s):  
Zhenguo Mu ◽  
Junfeng Yang
Keyword(s):  
Probability Distribution ◽  
Stochastic Programming ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Optimization Problems ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm ◽  
Fast Iterations

Stochastic programming is an approach for solving optimization problems with uncertainty data whose probability distribution is assumed to be known, and progressive hedging algorithm (PHA) is a well-known decomposition method for solving the underlying model. However, the per iteration computation of PHA could be very costly since it solves a large number of subproblems corresponding to all the scenarios. In this paper,  a stochastic variant of PHA is studied. At each iteration, only a small fraction of the scenarios are selected uniformly at random and the corresponding variable components are updated accordingly, while the variable components corresponding to those not selected scenarios are kept untouch. Therefore, the per iteration cost can be controlled freely to achieve very fast iterations. We show that, though the per iteration cost is reduced significantly, the proposed stochastic PHA converges in an ergodic sense at the same sublinear rate as the original PHA.

Birthday Distribution Problems

2013 ◽  
Vol 373-375 ◽  
pp. 1900-1905
Author(s):  
Man Li ◽  
Zhi Gang Zhang
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Monte Carlo Simulations ◽  
Frequency Distribution ◽  
Distribution Law ◽  
Distribution Problems

Based on the distinguishable ball-into-box issue, this paper started from a seemingly simple ball and extended to the question of birthday frequency distribution, i.e. people birthday in different dates probability distribution and the distribution law. In addition, the value was obtained by Monte Carlo simulations with different frequency distribution birthday days, finally when frequency simulation is large, achieving the theoretical value of the frequency values to estimate the probability,and the corresponding distribution can be obtained.

Nonlinear Stochastic Programming Involving CVaR in the Objective and Constraints

Informatica ◽  
2015 ◽  
Vol 26 (4) ◽  
pp. 569-591 ◽  
Author(s):  
Valerijonas Dumskis ◽  
Leonidas Sakalauskas
Keyword(s):  
Stochastic Programming

GAS-PHASE PROBABILITY DISTRIBUTION IN LIQUID CROSS-FLOW

2014 ◽  
Vol 26 (3) ◽  
pp. 229-260 ◽  
Author(s):  
Miguel A. Balzan ◽  
Brian A. Fleck
Keyword(s):  
Probability Distribution ◽  
Gas Phase ◽  
Cross Flow ◽  
Phase Probability Distribution

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

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