Robust Solutions to Constrained Optimization Problems with Uncertain Parameters

William Marsh Rice University, Houston TX

Investigators

Abstract

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 such as space exploration.