• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Solving ellipsoidal inclusion and optimal experimental design problems: Theory and algorithms.
【24h】

Solving ellipsoidal inclusion and optimal experimental design problems: Theory and algorithms.

机译：解决椭球包含问题和最佳实验设计问题：理论和算法。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This thesis is concerned with the development and analysis of Frank-Wolfe type algorithms for two problems, namely the ellipsoidal inclusion problem of optimization and the optimal experimental design problem of statistics. These two problems are closely related to each other and can be solved simultaneously as discussed in Chapter 1 of this thesis.;Chapter 1 introduces the problems in parametric forms. The weak and strong duality relations between them are established and the optimality criteria are derived. Based on this discussion, we define epsilon-primal feasible and epsilon-approximate optimal solutions: these solutions do not necessarily satisfy the optimality criteria but the violation is controlled by the error parameter epsilon and can be arbitrarily small.;Chapter 2 deals with the most well-known special case of the optimal experimental design problems: the D-optimal design problem and its dual, the Minimum-Volume Enclosing Ellipsoid (MVEE) problem. Chapter 3 focuses on another special case, the A-optimal design problem. In Chapter 4 we focus on a generalization of the optimal experimental design problem in which a subset but not all of parameters is being estimated. We focus on the following two problems: the Dk-optimal design problem and the A k-optimal design problem, generalizations of the D-optimal and the A-optimal design problems, respectively. In each chapter, we develop first-order algorithms for the respective problem and discuss their global and local convergence properties. We present various initializations and provide some computational results which confirm the attractive features of the first-order methods discussed.;Chapter 5 investigates possible combinatorial extensions of the previous problems. Special attention is given to the problem of finding the Minimum-Volume Ellipsoid (MVE) estimator of a data set, in which a subset of a certain size is selected so that the minimum-volume ellipsoid enclosing these points has the smallest volume. We discuss how the algorithms in Chapter 2 can be adapted in order to attack this problem. Many efficient heuristics and a branch-and-bound algorithm are developed.
机译：本文针对Frank-Wolfe型算法的开发和分析，针对两个问题，即优化的椭球包含问题和统计的最优实验设计问题进行了研究。这两个问题彼此密切相关，可以按照本文的第1章中的描述同时解决。第1章以参数形式介绍了这些问题。建立它们之间的弱对偶关系和强对偶关系，并推导最佳准则。在此讨论的基础上，我们定义了epsilon-primal可行方案和epsilon-approximately最优方案：这些方案不一定满足最优性准则，但违规行为则由误差参数epsilon控制，并且可以任意小。第二章讨论了大多数最优实验设计问题的著名特例：D最优设计问题及其对偶的最小体积封闭椭球（MVEE）问题。第3章重点讨论另一种特殊情况，即A最优设计问题。在第四章中，我们着重于最佳实验设计问题的一般化，在该问题中，正在估计一个子集而不是所有参数。我们关注以下两个问题：Dk最优设计问题和A k最优设计问题，D最优设计和A最优设计问题的推广。在每一章中，我们针对各自的问题开发一阶算法，并讨论它们的全局和局部收敛性。我们提出了各种初始化方法，并提供了一些计算结果，这些结果证实了所讨论的一阶方法的吸引人的特征。第五章研究了先前问题的可能组合扩展。特别注意寻找数据集的最小体积椭球（MVE）估计器的问题，其中选择了某个大小的子集，以便包围这些点的最小体积椭球具有最小的体积。我们将讨论如何修改第2章中的算法以解决此问题。开发了许多有效的启发式方法和分支定界算法。

著录项

  • 作者

    Ahipasaoglu, Selin Damla.;

  • 作者单位

    Cornell University.;

  • 授予单位 Cornell University.;
  • 学科 Operations Research.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 146 p.
  • 总页数 146
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号