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

数学科学：梯度投影方法、拉格朗日增广技术以及最优控制问题的充分条件

• 批准号: 9205240
• 负责人: Joseph Dunn
• 金额: $ 6万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205240&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Gradient; Projection; Methods

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.

该项目有四个主要目标：i）为具有状态和控制变量约束的大规模离散时间控制问题以及类似连续时间问题的有限差分近似确定有效的乘法器更新实现； ii) 将现有的收敛分析扩展到具有无限维范围空间的不等式约束问题； iii) 开发主题算法和其他约束最小化方法的收敛分析所需的 Kuhn-Tucker 充分条件的无限维扩展； iv) 研究产生缩放算子的拟牛顿递归，这些缩放算子自动具有良好的全局和渐近属性。 该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操作中的重要应用相关。