Four Mathematical Programming Paradigms with Operations Research Applications

运筹学应用的四种数学编程范式

• 批准号: 0969600
• 负责人: Angelia Nedich
• 金额: $ 24万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0969600&HistoricalAwards=false
• 关键词: Four; Mathematical; Programming; Paradigms; Operations

This proposal aims at investigating four emerging modeling paradigmsin mathematical programming that have gained increased attention in recent years due to their pervasive applications in operations research and other engineering fields as well as in economics and finance, but which have yet to receive wide popularity and lack focused research. These paradigms are: competition, dynamics, hierarchy, and inverse problems. The objective of the project is to develop a comprehensive and rigorous foundation for the sustained treatment and applications of these paradigms in the context of complex engineering and economic systems. The proposed approach is to study the mathematical formulations of these paradigms in terms of extended mathematical and equilibrium programs, constrained continuous-time dynamical systems, and multi-agent and multi-level optimization. Novel mathematical theories and advanced computational tools will be developed. This will require the combined methodology of continuous and disjunctive programming, global optimization, continuous- and discrete-time dynamical systems theory, and contemporary mathematical tools such as variational and set-valued analysis.If successful, the results of the proposed research will lead to improved understanding and efficient solution of highly complex engineering, economic, and biological systems characterized by four intrinsic elements: competition among multiple selfish agents, time evolution prior to the attainment of an optimum or equilibrium, hierarchical structure of the optimizing agents, and historical and/or observed data that need to be respected. Due to its interdisciplinary nature, the proposed activity offers an opportunity to bring together experts in diverse disciplines to advance their individual fields and make joint contributions to significant societal problems such as efficient resource allocation in engineering and economic systems, congestion in transportation systems, and resolution of conflicts among competing selfish agents, to name a few areas of applications.

该建议旨在调查四个新兴的建模范例数学编程，这些编程近年来由于其在运营研究和其他工程领域以及经济学和金融领域的普遍应用而引起了人们的关注，但尚未获得广泛的受欢迎程度和缺乏专注的研究。 这些范式是：竞争，动态，层次结构和反问题。 该项目的目的是为在复杂的工程和经济体系的背景下为这些范式的持续治疗和应用建立一个全面而严格的基础。 提出的方法是根据扩展的数学和平衡程序，约束的连续时间动力学系统以及多级和多级优化来研究这些范式的数学公式。 将开发新颖的数学理论和高级计算工具。 这将需要持续和脱节的编程，全球优化，连续和离散的时间动态系统理论以及当代数学工具（例如变异和设定值分析）的综合方法。如果成功的结果将导致高度复杂的工程，经济和生物学的竞争，以改善高度的理解和有效的竞争，以改善高度的理解和有效的效果：优化剂的最佳或平衡，层次结构以及需要尊重的历史和/或观察到的数据。 由于其跨学科性质，该提议的活动提供了一个机会，可以将各种学科的专家汇集在一起​​，以推动其各个领域，并为重大社会问题做出共同贡献，例如工程和经济体系中有效的资源分配，运输系统中的拥堵以及竞争性的自私机构之间的冲突解决方案，以命名应用程序的一些领域。