Mathematical Sciences: Projected Newton Methods for Optimal Control Problems and Other Large-Scale Structured Nonlinear Programs

数学科学：最优控制问题和其他大规模结构化非线性程序的投影牛顿法

• 批准号: 8702929
• 负责人: Joseph Dunn
• 金额: $ 9.45万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702929&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projected; Newton; Methods

The investigation proposed here has as its main objective the design, analysis, and testing of the so called projected Newton methods in computational optimization, with a special emphasis on the application of these methods to optimal control problems. Two kinds of problems are considered: disrete-time dynamical optimization problems and continuous time problems. It seems likely that the results of this research may be also applicable to other large-scale structured nonlinear optimization problems. The projected Newton method algorithms converge more rapidly than the standard first order, i.e. gradient based methods, yet the associated per iteration computational costs are still only proportional to n, where n is the number of subintervals of the time interval under consideration. A sizeable portion of the per iteration work can be organized for parallel computation. This research belongs to computational methods in optimization and control. Problems of this type arise in many applications, typically in optimization of trajectories for space vehicles and in calculations of optimal programs for control computers for various industrial processes.

这里提出的调查的主要目标是 设计，分析和测试所谓的投影牛顿 方法在计算优化，特别强调 这些方法在最优控制问题中的应用。两 考虑了离散时间动力学问题 优化问题和连续时间问题。似乎 这项研究的结果可能也适用于 其他大规模结构化非线性优化问题。 投影牛顿法算法收敛更快 比标准的一阶方法，即基于梯度的方法， 相关的每次迭代计算成本仍然仅 其中n是子区间的数目， 考虑的时间间隔。相当大一部分的每 可以组织迭代工作以进行并行计算。 本研究属于计算方法， 优化与控制这种类型的问题出现在许多 应用，通常在空间轨道的优化中 车辆以及最佳控制程序的计算 用于各种工业过程的计算机。