Variational Conditions: Structure and Computation

变分条件:结构和计算

基本信息

  • 批准号:
    0305930
  • 负责人:
  • 金额:
    $ 17.74万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2003
  • 资助国家:
    美国
  • 起止时间:
    2003-06-01 至 2006-09-30
  • 项目状态:
    已结题

项目摘要

This project is focused on investigating the mathematical structure of certain classes of variational conditions, and designing and analyzing effective computational algorithms to solve them. Success in the proposed work would permit analysis to be done more simply, with better insight, and with greater exploitation of problem structure, for a broad class of equilibrium problems having substantial practical usefulness as well as intrinsic mathematical interest. It would also produce better computational algorithms, and the means for justifying them. Sub-topics in this research program include:- Gaining better insight into degeneracy and its effects through analysis of parameterized versions of variational conditions, with the aim of illuminating the effect of special structure on the sensitivity and stability behavior of the problem.- Developing new computational methods using approximate derivatives, justifying their convergence, and testing them computationally. - Improving convergence analysis for methods of linearization type, and applying that analysis to, e.g., the computational methods discussed just above. - Analyzing specially structured variational conditions using methods of composition duality combined with the new stability and sensitivity information developed in this project.- Applying knowledge gained in the above research to analysis of other promising areas such as quasi-variational inequalities.Variational conditions are mathematical models of equilibrium problems. They are useful for a wide variety of problems from areas including economic policy studies, agricultural economics, structural engineering, transportation, materials science, game theory (that is, models of conflict), and others. One of the reasons why these problems are especially hard is that they model situations in which individuals or groups are not acting in concert, and indeed are often acting at cross purposes. For example, in a road traffic equilibrium problem each driver is trying to find a route that is best for him or her, but the effects of many drivers' independent choices can make conditions bad for everyone (e.g., by creating congestion on popular routes). The research that is proposed will try to develop more knowledge about how mathematical models can represent these problems, what the properties of those models are, and how to use those properties to compute numerical solutions to the models. With such knowledge the models could then be used to answer "what-if" questions and thus to design better management methods. For example, civil engineers interested in improving traffic flow might use such models to predict more accurately the effect of improving existing roads or of building new roads, and thereby determine how best to spend a limited budget to reduce traffic congestion.
该项目的重点是研究某些类别的变分条件的数学结构,并设计和分析有效的计算算法来解决它们。成功地在拟议的工作将允许分析做得更简单,更好的洞察力,并与更大的利用问题的结构,为广泛的一类平衡问题具有实质性的实际用途,以及内在的数学兴趣。它还将产生更好的计算算法,以及证明它们的方法。该研究计划的子课题包括:-通过分析变分条件的参数化版本,更好地了解退化及其影响,目的是阐明特殊结构对问题的敏感性和稳定性行为的影响。 使用近似导数开发新的计算方法,证明其收敛性,并进行计算测试。 - 改进线性化类型方法的收敛性分析,并将该分析应用于,例如,上面讨论的计算方法。- 使用组合对偶方法结合本项目开发的新稳定性和灵敏度信息分析特殊结构的变分条件。将上述研究中获得的知识应用于分析其他有前途的领域,如拟变分不等式。变分条件是平衡问题的数学模型。它们对经济政策研究、农业经济学、结构工程、运输、材料科学、博弈论(即冲突模型)等领域的各种问题都很有用。这些问题之所以特别困难,原因之一是它们模拟的情况是,个人或群体的行动并不一致,实际上往往是出于不同的目的。例如,在道路交通平衡问题中,每个驾驶员都试图找到最适合他或她的路线,但是许多驾驶员的独立选择的影响可能使条件对每个人都不利(例如,通过在热门路线上造成拥堵)。提出的研究将试图开发更多的知识,关于数学模型如何表示这些问题,这些模型的属性是什么,以及如何使用这些属性来计算模型的数值解。有了这些知识,模型就可以用来回答“假设”问题,从而设计出更好的管理方法。例如,对改善交通流量感兴趣的土木工程师可以使用这样的模型来更准确地预测改善现有道路或建造新建道路的效果,从而确定如何最好地花费有限的预算来减少交通拥堵。

项目成果

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专利数量(0)

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Stephen Robinson其他文献

The thermic response to food is related to sensitivity to adrenaline in a group at risk for the development of type II diabetes
对于有患 II 型糖尿病风险的人群来说,对食物的热反应与对肾上腺素的敏感性有关
  • DOI:
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    4.7
  • 作者:
    Shareen Forbes;Stephen Robinson;Kim H. Parker;Ian A. Macdonald;Mark I. McCarthy;Desmond G. Johnston
  • 通讯作者:
    Desmond G. Johnston
Increased leucine turnover in women during the third trimester of uncomplicated pregnancy.
在无并发症的妊娠晚期,女性的亮氨酸周转率增加。
  • DOI:
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    M. Jolly;J. Bertie;R. Gray;P. Bannister;S. Venkatesan;Desmond G. Johnston;Stephen Robinson
  • 通讯作者:
    Stephen Robinson
149 Feedback from publication of ‘Making an accurate diagnosis of anterior mediastinal lesions: a proposal for a new diagnostic algorithm from the BTOG Thymic Malignancies Specialist Interest Group’
149. 《关于“精确诊断前纵隔病变:英国胸科肿瘤学会胸腺恶性肿瘤专业兴趣小组提出的新诊断算法建议”发表的反馈》
  • DOI:
    10.1016/j.lungcan.2025.108259
  • 发表时间:
    2025-02-01
  • 期刊:
  • 影响因子:
    4.400
  • 作者:
    Rebecca Duerden;Matthew Evison;Stephen Robinson;Anna Sharman;Shalini Datta;Kanadai Rammohan;Maria Angeles Montero-Fernandez;David Gilligan;British Thoracic Oncology Group (BTOG) Thymic Malignancies Specialist Interest Group, on behalf of
  • 通讯作者:
    British Thoracic Oncology Group (BTOG) Thymic Malignancies Specialist Interest Group, on behalf of
Scene complexity and the detail trace of human long-term visual memory
  • DOI:
    10.1016/j.visres.2024.108525
  • 发表时间:
    2025-02-01
  • 期刊:
  • 影响因子:
  • 作者:
    Cameron Kyle-Davidson;Oscar Solis;Stephen Robinson;Ryan Tze Wang Tan;Karla K. Evans
  • 通讯作者:
    Karla K. Evans
Non-contact mapping guided cardiac resynchronization therapy for a failing systemic right ventricle.
非接触式测绘引导心脏再同步治疗衰竭的全身性右心室。

Stephen Robinson的其他文献

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{{ truncateString('Stephen Robinson', 18)}}的其他基金

SEARCDE 2012 Conference
SEARCDE 2012 会议
  • 批准号:
    1230997
  • 财政年份:
    2012
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Standard Grant
TTU STEM Majors for Rural Teaching (TTU-SMaRT) - Noyce Scholarship Program
TTU STEM 农村教学专业 (TTU-SMaRT) - 诺伊斯奖学金计划
  • 批准号:
    1136403
  • 财政年份:
    2011
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Standard Grant
Computation and Theory for a Class of Nonsmooth Functions
一类非光滑函数的计算与理论
  • 批准号:
    9109345
  • 财政年份:
    1992
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Continuing Grant
Computation and Theory in Decentralized Optimization
分散优化中的计算和理论
  • 批准号:
    8801489
  • 财政年份:
    1988
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Continuing Grant
Computational Approximation of Optimization Problems (Computer Research)
优化问题的计算逼近(计算机研究)
  • 批准号:
    8502202
  • 财政年份:
    1985
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Continuing Grant
Symposium on Analysis and Computation of Fixed Points; Madison, Wisconsin, May 7-8, 1979
不动点分析与计算研讨会;
  • 批准号:
    7907217
  • 财政年份:
    1979
  • 资助金额:
    $ 17.74万
  • 项目类别:
    Standard Grant

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职业:极端​​水动力条件下沿海流固耦合的开源 GPU 加速计算基础设施
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