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

该项目将发展针对混合计算方案的分析和数值研究，使用拉格朗日增广技术隐式地处理复杂约束问题，并使用梯度投影方法显式地处理简单约束。这些研究的动机是最优控制中的问题，其中需要解决受特殊数学结构约束的大型方程组。最优控制问题在工程和自然科学中自然出现。

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.