Mathematical Sciences: Gradient Projection Methods, Lagrangian Augmentation Techniques, and Sufficient Conditions for Optimal Control Problems

该项目有四个主要目标：i）确定 用于大规模的有效乘法器更新实现 具有状态和控制变量的离散时间控制问题 约束，并为有限差分近似， 2.类似的连续时间问题; 2）扩展现有的 收敛分析的问题与不等式约束， 有无限维的范围空间; iii）发展 Kuhn-Tucker充分 该主题收敛分析所需的条件 算法和其他约束最小化方法; iv）研究产生标度的拟牛顿递归 自动具有良好行为的全局和 渐近性质 在这个项目中研究的算法涉及到 在飞机运行中的重要应用， 航天器、电力网络、化学和核 反应堆、机械手和生态系统。

This project has four main objectives: i) to identify efficient multiplier update implementations for large scale discrete-time control problems with state and control variable constraints, and for finite-difference approximations to analogous continuous-time problems; ii) to extend existing convergence analyses to problems with inequality constraints that have infinite-dimensional range spaces; iii) to develop infinite-dimensional extensions of the Kuhn-Tucker sufficient conditions needed in convergence analyses for the subject algorithms and other constrained minimization methods as well; iv) to investigate quasi-Newton recursions that produce scaling operators which automatically possess well-behaved global and asymptotic properties. The algorithms investigated in this project are related to significant applications in the operation of aircraft and spacecraft, electrical power networks, chemical and nuclear reactors, robot manipulators, and ecosystems.