Optimization: Theory, Algorithms, and Applications

优化：理论、算法和应用

• 批准号: 9971852
• 负责人: James Burke
• 金额: $ 10.5万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971852&HistoricalAwards=false
• 关键词: Optimization; Theory; Algorithms; Applications

9971852BurkeTwo topics are proposed for study: (1) the variational analysis of eigenvalue functions and (2) non-parametric population analysis. In the first topic the principal investigator will apply modern techniques of nonsmooth analysis and variational geometry to study the variational properties of certain functions of the spectrum on the space of n x n complex valued matrices, e.g., the spectral abscissa and the spectral radius. In the second topic, the principal investigator intends to analyze and develop algorithmic solution techniques for the non-parametric version of the basic problem of population analysis. Specifically, the principal investigator intends to use maximum likelihood techniques to estimate the underlying probability measure associated with population variability.Understanding the variational behavior of the spectrum of matrix valued mappings is essential to our understanding and control of discrete and continuous dynamical systems. Such systems arise in numerous practical applications ranging from the design of structures that can withstand a major earthquake to flight control for modern aircraft. The results of the principal investigator's research program are intended to make possible for the first time the derivation of optimality and/or equilibrium conditions for numerous problems associated with spectral variations that occur in numerous engineering applications. On the other hand, population analysis is the statistical methodology used to understand inter-subject variability in studies designed to analyze a phenomenon associated with a targeted population. For example, the methodology is widely used in pharmocokinetic studies since it is the key to understanding how drugs behave in humans and animals. The principal investigator intends to analyze and develop algorithmic solution techniques for the non-parametric version of this problem. The goal is to incorporate these algorithms into a software package now being developed by the Resource Facility for Population Kinetics at the University of Washington.

提出了9971852Burketwo主题进行研究：（1）特征值函数的变异分析和（2）非参数人群分析。在第一个主题中，主要研究者将应用非平滑分析和变分几何形状的现代技术来研究光谱在n x n复合物有价值矩阵的空间上的某些功能的变异性质，例如光谱横坐标和光谱半径。在第二个主题中，主要研究者打算分析和开发针对人口分析基本问题的非参数版本的算法解决方案技术。具体而言，主要研究者打算使用最大的似然技术来估计与人口变异性相关的潜在概率措施。理解矩阵有价值映射的频谱的变异行为对于我们对离散和持续动态系统的理解和控制至关重要。这种系统出现在许多实际应用中，包括可以承受重大地震的结构的设计到现代飞机的飞行控制。首席研究者研究计划的结果旨在首次成为与许多工程应用中发生的频谱变化相关的许多问题的最佳和/或平衡条件的推导。另一方面，人口分析是用于了解用于分析与目标人群相关的现象的研究中的统计方法。例如，该方法被广泛用于药代动力学研究中，因为它是了解药物在人类和动物中的行为的关键。首席研究人员打算分析和开发该问题的非参数版本的算法解决方案技术。目的是将这些算法纳入华盛顿大学的人群动力学的资源设施正在开发的软件包中。