RIA:Complexity Analysis and Optimal Algorithms for NonlinearProblems

RIA:非线性问题的复杂性分析和优化算法

基本信息

  • 批准号:
    8809022
  • 负责人:
  • 金额:
    $ 5.71万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1988
  • 资助国家:
    美国
  • 起止时间:
    1988-06-01 至 1990-11-30
  • 项目状态:
    已结题

项目摘要

This proposal involves complexity analysis and the development of optimal algorithms for the solution of nonlinear problems. Unlike most current research in complexity which is discrete in nature, the problems considered in this proposal are (piecewise) continuous functions of one or more real variables. The tools for complexity analysis of these problems thus differ from traditional complexity analysis and are based on the ideas of information-based complexity. The development of an upper bound on problem complexity is similar to classical numerical analysis (and may in fact borrow from previous work therein). The derivation of lower bounds on a problem's complexity is one of the novel aspects of this research, and can be roughly described as follows: Using mathematical techniques, one develops a set of functions with different solutions to the problem but which are indistinguishable using a given amount of information. Unless this set of functions is a singleton no algorithm can solve the problem. This provides lower bounds on the amount of information required to solve the problems, which in turn bounds the problem complexity from below. While the concepts are simple, the derivation of a particular bound is generally quite difficult, and often provides insight useful for achieving better upper bounds. The nonlinear problems addressed in this research will include both worst-case and "average"-case analysis of the computation of topological degree in one or more dimensions, root-finding for Lipschitz function in one two and three dimensions, and segmentation/reconstruction of overlapping functions from function values (with restrictions from computer vision). These problems have both theoretical and practical importance, and the techniques developed for their analysis should be useful elsewhere.
这一建议涉及复杂性分析和最优算法的发展,以解决非线性问题。与目前大多数复杂性研究本质上是离散的不同,本建议考虑的问题是一个或多个实变量的(分段)连续函数。因此,用于这些问题的复杂性分析的工具不同于传统的复杂性分析,而是基于基于信息的复杂性的思想。问题复杂性上界的发展与经典数值分析类似(实际上可能借鉴了先前的工作)。问题复杂性下界的推导是本研究的一个新颖方面,大致可以描述如下:使用数学技术,开发一组具有问题不同解的函数,但在给定信息量的情况下,这些函数是不可区分的。除非这组函数是单例的,否则没有任何算法可以解决这个问题。这为解决问题所需的信息量提供了下限,从而限制了问题的复杂度。虽然概念很简单,但特定边界的推导通常相当困难,并且通常提供对获得更好的上界有用的见解。本研究解决的非线性问题将包括一个或多个维度拓扑度计算的最坏情况和“平均”情况分析,一维、二维和三维Lipschitz函数的寻根,以及从函数值中分割/重建重叠函数(受计算机视觉的限制)。这些问题具有理论和实践的重要性,为分析这些问题而开发的技术应该在其他地方有用。

项目成果

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Terrance Boult其他文献

Towards comparable cross-sector risk analyses: A re-examination of the Risk Analysis and Management for Critical Asset Protection (RAMCAP) methodology
  • DOI:
    10.1016/j.ijcip.2016.05.001
  • 发表时间:
    2016-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    Richard White;Aaron Burkhart;Randy George;Terrance Boult;Edward Chow
  • 通讯作者:
    Edward Chow

Terrance Boult的其他文献

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{{ truncateString('Terrance Boult', 18)}}的其他基金

SCH: INT: Collaborative Research: Learning and Sensory-based Modeling for Adaptive Web-Empowerment Trauma Treatment
SCH:INT:协作研究:自适应网络赋权创伤治疗的学习和基于感觉的建模
  • 批准号:
    1418520
  • 财政年份:
    2014
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Standard Grant
RI: Small: Open Vision - Tools for Open Set Computer Vision and Learning
RI:小型:开放视觉 - 用于开放集计算机视觉和学习的工具
  • 批准号:
    1320956
  • 财政年份:
    2013
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Standard Grant
PFI: I SEE: Innovation through Synergistic Educational Engagement
PFI:我看到:通过协同教育参与进行创新
  • 批准号:
    0650251
  • 财政年份:
    2008
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Standard Grant
PYI: 3-D Computer Vision
PYI:3D 计算机视觉
  • 批准号:
    9496310
  • 财政年份:
    1994
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Continuing Grant
Acquisition of Giga-Op Simulation/Computation Environment to Support Electrical Engineering and Computer Science Research at Lehigh University
收购 Giga-Op 仿真/计算环境以支持理海大学的电气工程和计算机科学研究
  • 批准号:
    9413782
  • 财政年份:
    1994
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Standard Grant
Real-Time Active Acquisition and Representation of 3-Dimensional Objects
3 维物体的实时主动采集和表示
  • 批准号:
    9022468
  • 财政年份:
    1991
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Standard Grant
PYI: 3-D Computer Vision
PYI:3D 计算机视觉
  • 批准号:
    9057951
  • 财政年份:
    1990
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Continuing Grant
Research in Acquisition of Three Dimensional Information
三维信息获取研究
  • 批准号:
    8800370
  • 财政年份:
    1988
  • 资助金额:
    $ 5.71万
  • 项目类别:
    Continuing Grant

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  • 批准号:
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