Robust Solutions to Constrained Optimization Problems with Uncertain Parameters

在这项研究中，研究人员将最近的鲁棒优化方法扩展到一般的优化问题，包括不确定等式约束的非线性规划。 扩展提供了一个坚实的基础，严格对待不确定参数在一般的优化问题，合理的参数估计存在和不确定变化的幅度是温和的。 本研究将集中研究和开发合适的优化策略、有效的数值算法和方便的软件工具，为处理一般约束优化设置中的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，往往存在物理量（参数）的值不能总是精确测量。 在关键应用中，必须小心处理这种不确定性，同时尝试实现尽可能好的性能，以防止在最坏情况下发生系统故障。 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。 研究成果将有可能应用于空间探索等广泛领域。

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.