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New results in stochastic programming under incomplete information.

机译：信息不完全的情况下随机规划的新结果。

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摘要

In this dissertation, we consider two different kinds of stochastic programming problem under incomplete information. In Chapters 2 to 7, multivariate probability distributions with given marginals are considered, along with linear functionals, to be minimized or maximized, acting on them. The functionals are supposed to satisfy the Monge or inverse Monge or some higher order convexity property and they may be only partially known. Existing results in connection with Monge arrays are reformulated and extended in terms of LP dual feasible bases. Lower and upper bounds are given for the optimum value as well as for unknown coefficients of the objective function based on the knowledge of some dual feasible bases and corresponding objective function coefficients. In the two- and three-dimensional cases dual feasible bases are obtained for the problem, where not only the univariate marginals, but also the covariances of the pairs of random variables are known.; In Chapters 8 and 9, an LP is considered where the technology coefficients are unknown and random samples are taken to estimate them. A stochastic programming problem is formulated to find the optimal sample sizes where it is required that a confidence interval should cover the unknown deterministic optimum value by a given probability and the cost of sampling be minimum.
机译：本文考虑了信息不完全情况下的两种随机规划问题。在第2章至第7章中，考虑具有给定边际的多元概率分布以及线性函数，对其进行最小化或最大化。这些函数应该满足蒙奇或逆蒙奇或更高阶的凸性，并且它们可能仅是部分已知的。关于Monge阵列的现有结果将根据LP对偶可行基础进行重新制定和扩展。基于一些对偶可行基和相应的目标函数系数的知识，给出了目标函数的最佳值以及未知系数的上下限。在二维和三维情况下，针对该问题获得了两个可行的基础，不仅已知单变量边际，而且还知道了随机变量对的协方差。在第8章和第9章中，考虑了技术系数未知的LP，并采用随机样本对其进行估计。在需要置信区间应以给定的概率覆盖未知的确定性最佳值并且采样成本最小的情况下，制定了一个随机规划问题以找到最佳样本量。

著录项

  • 作者

    Hou, Xiaoling.;

  • 作者单位

    Rutgers The State University of New Jersey - New Brunswick.;

  • 授予单位 Rutgers The State University of New Jersey - New Brunswick.;
  • 学科 Operations Research.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 p.606
  • 总页数 100
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 运筹学;
  • 关键词

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