AF: Medium: Collaborative Research: On the Power of Mathematical Programming in Combinatorial Optimization
AF:媒介:协作研究:论组合优化中数学规划的力量
基本信息
- 批准号:1407779
- 负责人:
- 金额:$ 36.74万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2014
- 资助国家:美国
- 起止时间:2014-09-01 至 2018-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Mathematical programming is a powerful tool for attacking combinatorial problems. One transforms a discrete task into a related continuous one by casting it as optimization over a convex body. Linear and semi-definite programming (LP and SDP) form important special cases and are central tools in the theory and practice of combinatorial optimization. These approaches have achieved spectacular success in computing approximately optimal solutions for problems where finding exact solutions is computationally intractable.While there are very strong bounds known on the efficacy of particular families of relaxations, it remains possible that adding a small number of variables or constraints could lead to drastically improved solutions. We propose the development of a theory to unconditionally capture the power of LPs and SDPs without any complexity-theoretic assumptions. Our approach has the potential to show something remarkable: For many well-known problems, the basic LP or SDP is optimal among a very large class of algorithms. More concretely, we suggest a method that could rigorously characterize the power of polynomial-size LPs and SDPs for a variety of combinatorial optimization tasks. This involves deep issues at the intersection of many areas of mathematics and computer science, with the ultimate goal of significantly extending our understanding of efficient computation.Mathematical programming is of major importance to many fields---this is especially true for computer science and operations research. These methods have also seen dramatically increasing use in the analysis of "big data" from across the scientific spectrum. From a different perspective, LPs and SDPs can be thought of as rich proof systems, and characterizing their power is a basic problem in the theory of proof complexity. Thus the outcomes of the proposed research are of interest to a broad community of scientists, mathematicians, and practitioners.
数学规划是解决组合问题的有力工具。通过将离散任务转化为凸体上的优化问题,将离散任务转化为相关的连续任务。线性规划和半定规划(LP和SDP)是组合优化的重要特例,是组合优化理论和实践的核心工具。这些方法在计算精确解困难的问题的近似最优解方面取得了惊人的成功。虽然已知关于特定松弛族的有效性的非常强的界,但添加少量的变量或约束仍有可能导致解的显著改善。我们建议发展一种理论,在没有任何复杂性理论假设的情况下无条件地捕捉LP和SDP的力量。我们的方法有可能展示一些值得注意的东西:对于许多众所周知的问题,基本的LP或SDP在非常大的一类算法中是最优的。更具体地说,我们提出了一种方法,它可以严格地刻画多项式大小的LP和SDP对于各种组合优化任务的能力。这涉及许多数学和计算机科学领域交叉的深层次问题,最终目的是大大扩展我们对高效计算的理解。数学编程对许多领域都很重要-对于计算机科学和运筹学研究更是如此。这些方法在科学领域的“大数据”分析中的使用也大幅增加。从不同的角度来看,LP和SDP可以被认为是丰富的证明系统,刻画它们的能力是证明复杂性理论中的一个基本问题。因此,拟议研究的结果引起了广大科学家、数学家和实践者的兴趣。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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James Lee其他文献
Will China’s Rise Be Peaceful? A Social Psychological Perspective
中国的崛起会是和平的吗?
- DOI:
10.1080/14799855.2016.1140644 - 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
James Lee - 通讯作者:
James Lee
Triple-Combination Therapy with Olmesartan, Amlodipine, and Hydrochlorothiazide in Black and Non-Black Study Participants with Hypertension
奥美沙坦、氨氯地平和氢氯噻嗪对黑人和非黑人高血压研究参与者的三联疗法
- DOI:
- 发表时间:
2012 - 期刊:
- 影响因子:3
- 作者:
S. Chrysant;T. Littlejohn;J. L. Izzo;D. Kereiakes;S. Oparil;M. Melino;James Lee;Victor Fernandez;R. Heyrman - 通讯作者:
R. Heyrman
SUN13837 in Treatment of Acute Spinal Cord Injury, the ASCENT-ASCI Study
SUN13837 治疗急性脊髓损伤,ASCENT-ASCI 研究
- DOI:
10.11648/j.cnn.20180201.11 - 发表时间:
2018 - 期刊:
- 影响因子:6
- 作者:
B. Levinson;James Lee;H. Chou;D. Maiman - 通讯作者:
D. Maiman
Shared Mental Models Among Clinical Competency Committees in the Context of Time-Variable-Competency-Based Advancement to Residency.
在基于时间变量的能力提升为住院医师的背景下,临床能力委员会之间的共享思维模型。
- DOI:
10.1097/acm.0000000000003638 - 发表时间:
2020 - 期刊:
- 影响因子:7.4
- 作者:
A. Schwartz;D. Balmer;Emily C Borman;Alan Chin;Duncan Henry;B. Herman;Patricia M Hobday;James Lee;Sara M. Multerer;Ross E. Myers;K. Ponitz;A. Rosenberg;J. Soep;Daniel C. West;R. Englander - 通讯作者:
R. Englander
Abuse potential of mirogabalin in recreational polydrug users
米洛巴林在娱乐性多种药物使用者中的滥用可能性
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:4.4
- 作者:
J. Mendell;N. Levy‐Cooperman;E. Sellers;B. Vince;D. Kelsh;James Lee;V. Warren;H. Zahir - 通讯作者:
H. Zahir
James Lee的其他文献
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{{ truncateString('James Lee', 18)}}的其他基金
UKRI AHRC Impact Acceleration Account
UKRI AHRC 影响力加速账户
- 批准号:
AH/X003574/1 - 财政年份:2022
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
Air quality benefits from multi-year changes in post-pandemic working and travel patterns
空气质量受益于大流行后工作和旅行模式的多年变化
- 批准号:
NE/W00481X/1 - 财政年份:2021
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
AF: Small: Metric Information Theory, Online Learning, and Competitive Analysis
AF:小:度量信息论、在线学习和竞争分析
- 批准号:
2007079 - 财政年份:2020
- 资助金额:
$ 36.74万 - 项目类别:
Standard Grant
Atmospheric Composition and Radiative forcing effects_due to UN International Ship Emissions regulations
大气成分和辐射强迫效应_根据联合国国际船舶排放法规
- 批准号:
NE/S004564/1 - 财政年份:2019
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
AF: Small: Entropy Maximization in Approximation, Learning, and Complexity
AF:小:近似、学习和复杂性中的熵最大化
- 批准号:
1616297 - 财政年份:2016
- 资助金额:
$ 36.74万 - 项目类别:
Standard Grant
Megacity Delhi atmospheric emission quantification, assessment and impacts (DelhiFlux)
德里特大城市大气排放量化、评估和影响 (DelhiFlux)
- 批准号:
NE/P01643X/1 - 财政年份:2016
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
Sources and Emissions of Air Pollutants in Beijing
北京大气污染物来源及排放
- 批准号:
NE/N006917/1 - 财政年份:2016
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
AF: Small: Metric Geometry for Combinatorial Problems
AF:小:组合问题的度量几何
- 批准号:
1217256 - 财政年份:2012
- 资助金额:
$ 36.74万 - 项目类别:
Standard Grant
ClearfLo: Clean Air for London
ClearfLo:伦敦清洁空气
- 批准号:
NE/H003223/1 - 财政年份:2010
- 资助金额:
$ 36.74万 - 项目类别:
Research Grant
AF: Small: Spectral analysis, spectral algorithms, and beyond
AF:小型:光谱分析、光谱算法等
- 批准号:
0915251 - 财政年份:2009
- 资助金额:
$ 36.74万 - 项目类别:
Standard Grant
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2402837 - 财政年份:2024
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