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

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.

在本研究中，研究者将把最近的鲁棒优化方法扩展到一般优化问题，包括具有不确定等式约束的非线性程序。 该扩展为严格处理一般优化问题中的不确定参数提供了坚实的基础，其中存在合理的参数估计并且不确定变化的幅度适中。 所提出的研究将重点研究和开发合适的优化策略、高效的数值算法和方便的软件工具，为在一般约束优化设置中处理参数不确定性提供指导。在航天器等复杂系统的设计或控制中，经常会出现存在其值不能总是被精确测量的物理量（参数）。 在关键应用中，必须仔细处理此类不确定性，同时尝试实现尽可能好的性能，以防止最坏情况下的系统故障。 该项目将研究和开发严格的数学公式、计算机算法和软件工具，为处理参数不确定性提供指导。 研究结果可能适用于太空探索等广泛领域。