Robust Solutions to Constrained Optimization Problems with Uncertain Parameters

具有不确定参数的约束优化问题的鲁棒解决方案

• 批准号: 0405831
• 负责人: Yin Zhang
• 金额: $ 19.95万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405831&HistoricalAwards=false
• 关键词: Robust; Solutions; Constrained; Optimization; Problems; Robust; Solutions; Constrained; Optimization; Problems

In this research, the investigator will extend the recent robust optimization methodology to general optimization problems, including nonlinear programs with uncertain equality constraints. The extension provides a solid foundation for rigorously treating uncertain parameters in general optimization problems where reasonable parameter estimates exist and the magnitude of uncertain variations is moderate. The proposed research will focus on studying and developing suitable optimization strategies, efficient numerical algorithms and convenient software tools to provide guidelines for treating parameter uncertainties in a general constrained optimization setting.In the design or control of a complex system such as a spacecraft, there often exist physical quantities (parameters) whose values cannot always be precisely measured. In critical applications, such uncertainties must be carefully handled, while attempting to achieve as good a performance as possible, to prevent system failures under the worst-case scenario. This project will study and develop rigorous mathematical formulations, computer algorithms and software tools to provide guidelines for treating parameter uncertainties. The research findings will be potentially applicable to a wide range of fields suchas space exploration.

在这项研究中，研究者将将最近的强大优化方法扩展到一般优化问题，包括具有不确定平等限制的非线性程序。 该扩展为在存在合理参数估计的一般优化问题中严格处理不确定参数提供了坚实的基础，并且不确定变化的幅度中等。 拟议的研究将着重于研究和制定合适的优化策略，有效的数值算法和方便的软件工具，以提供在一般约束优化设置中处理参数不确定性的准则。在复杂系统（例如，诸如Spacecraft）的设计或控制中，通常存在物理量（参数），其值始终是精确测量的。 在关键应用中，必须仔细处理此类不确定性，同时试图取得尽可能出色的性能，以防止在最坏情况下进行系统故障。 该项目将研究和开发严格的数学配方，计算机算法和软件工具，以提供治疗参数不确定性的准则。 研究结果可能适用于这些空间探索的广泛领域。