Robust Solutions to Constrained Optimization Problems with Uncertain Parameters

在这项研究中，研究者将把最近的鲁棒优化方法扩展到一般的优化问题，包括具有不确定等式约束的非线性规划。该扩展为在存在合理参数估计且不确定变化幅度适中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。本研究将重点研究和开发合适的优化策略、高效的数值算法和便捷的软件工具，为处理一般约束优化设置中的参数不确定性提供指导。在设计或控制一个复杂的系统，如航天器，往往存在物理量（参数）的值不能总是精确测量。在关键应用程序中，必须小心处理这种不确定性，同时尽可能地实现良好的性能，以防止在最坏情况下出现系统故障。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。研究成果将有可能广泛应用于空间探索等领域。

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.