Mathematical Sciences: Gradient Projection and Lagrangian Augmentation Methods for Optimal Control and Other Large Scale Nonlinear Programs

该项目将开发针对混合计算方案的分析和数值研究，该混合计算方案使用拉格朗日增强技术隐式地处理具有复杂约束的问题，并使用梯度投影方法显式地处理较简单的约束。这些研究的动机是最优控制中的问题，在最优控制中，需要求解受特殊数学结构约束的大型方程组。最优控制问题自然而然地出现在工程和自然科学中。

This project will develop analytical and numerical studies directed at hybrid computational schemes that use Lagrangian augmentation technology to treat problems with intricate constraints implicitly, and gradient projection methods to handle simpler constraints explicitly. These studies are motivated by questions in optimal control where there is the need to solve large systems of equations subject to contraints with special mathematical structures. Optimal control problems arise naturally in engineering and natural sciences.