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)确定具有状态和控制变量约束的大规模离散时间控制问题的有效乘数更新实现，以及类似连续时间问题的有限差分近似；Ii)将现有的收敛分析扩展到具有无限维值域空间的不等式约束问题；iii)为主题算法和其他约束最小化方法的收敛分析提供Kuhn-Tucker充分条件的无限维扩展；iv)研究产生自动具有良好的全局和渐近性质的尺度算子的准牛顿递推。本项目研究的算法与飞机和航天器、电力网络、化学和核反应堆、机器人操纵器和生态系统的运行中的重要应用有关。

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.