Robust and Adaptive Optimization; a Tractable Approach to Optimization Under Uncertainty

这笔赠款用于a)为不确定情况下的多时段优化问题开发稳健和自适应的优化方法，b)将这些方法应用于美国在存在不利天气的空中交通管制中，以及c)在收入管理、定价和运输网络设计方面的应用。该方法将利用一系列广泛的方法，包括数学优化、模拟、控制理论、动力系统和博弈论的所有方面。从教育的角度来看，这笔拨款的结果将作为随机优化教学模块的组成部分，也将被收录在一本关于稳健优化的书中，该书渴望对该领域进行统一和现代的介绍。不确定条件下的多阶段优化是许多工程和管理问题的中心问题，如工程设计、供应链优化、财务规划、空中交通管制和收入管理。如果成功，这项研究的结果将有助于开发新的易处理和可扩展的方法来解决不确定条件下的优化问题，直接使用数据并通过上述书籍的出版也将影响本科生和研究生课程中教授不确定条件下的优化方法。作为测试案例，这项研究的结果将应用于美国在存在不利天气的情况下的空中交通管制。

This grant provides funding a) for the development of robust and adaptive optimization methods for multi-period optimization problems under uncertainty, b) for applications of these methods to air traffic control in the United States in the presence of adverse weather, and c) applications in revenue management, pricing and transportation network design. The approach will utilize a broad array of methodologies including all aspects of mathematical optimization, simulation, control theory, dynamical systems and game theory. From an educational standpoint, the results of this grant will serve as components in teaching modules on stochastic optimization and also be included in a book on robust optimization that aspires to present a unified and modern introduction to this area.Multi-period optimization under uncertainty is a central problem in many engineering and management problems, such as engineering design, supply chain optimization, financial planning, air traffic control and revenue management. If successful, the results of this research will enable the development of new tractable and scalable approaches to solving optimization under uncertainty using data directly and through the publication of the book mentioned above will also affect the way optimization under uncertainty is taught in both undergraduate and graduate curricula. As a test case, the results of this research will be applied to controlling air traffic in the United States in the presence of adverse weather.