Fast Sparse Nonlinear Optimization and Its Application to Optimal Control

快速稀疏非线性优化及其在最优控制中的应用

基本信息

批准号：
1522629
负责人：
William Hager
金额：
$ 24万
依托单位：
University of Florida
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-07-15 至 2019-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522629&HistoricalAwards=false
关键词：
Fast Sparse Nonlinear Optimization Its

项目摘要

New computational algorithms will be developed in this project for solving sparse optimization problems. These are large, complex problems that arise in science, engineering, and industry where the goal is to operate a large interconnected system in an efficient way. Applications range from power grids to air traffic control systems to the fabrication of computer chips. A specific application developed in the project is to optimal control which has a wide range of uses including space flight maneuvers, the optimal design of aerodynamic shapes, and the optimal design of manufacturing processes. The algorithms developed in the project for the sparse optimization problem provide solutions much faster and with much greater accuracy than was previously possible. The computational techniques developed in the project will be built around a new error estimator, which yields a tight bound for the error in a solution to an optimization problem in terms of the violation in the first-order optimality conditions, and a new dual-based approach to polyhedral projection. At the same time that the error in the solution is estimated, approximations to the dual multipliers at a stationary point are generated. The new polyhedral projection algorithm will be incorporated into a new algorithm for polyhedral constrained nonlinear optimization. With linearization and globalization techniques, the new algorithms will be used to achieve a fast and accurate solver for the general sparse constrained nonlinear optimization problem. The new optimization framework will be used to develop hp-orthogonal collocation techniques for solving optimal control problems. The research will focus on mesh refinement techniques for which the fast and accurate optimization solver will be instrumental in advancing the technology.

该项目将开发新的计算算法来解决稀疏优化问题。这些是科学、工程和工业中出现的大而复杂的问题，其目标是以有效的方式运行大型互连系统。应用范围从电网到空中交通控制系统再到计算机芯片的制造。该项目开发的一个具体应用是最优控制，其用途广泛，包括太空飞行机动、气动形状的优化设计以及制造工艺的优化设计。该项目中针对稀疏优化问题开发的算法比以前更快、更准确地提供了解决方案。该项目中开发的计算技术将围绕一个新的误差估计器构建，该误差估计器在违反一阶最优性条件的情况下为优化问题的解决方案中的误差产生严格的界限，以及一个新的基于对偶的误差估计器。多面体投影的方法。在估计解中的误差的同时，生成驻点处的双乘子的近似值。新的多面体投影算法将被纳入多面体约束非线性优化的新算法中。通过线性化和全球化技术，新算法将用于实现一般稀疏约束非线性优化问题的快速准确求解器。新的优化框架将用于开发 HP 正交配置技术来解决最优控制问题。该研究将重点关注网格细化技术，快速而准确的优化求解器将有助于推进该技术。

项目成果

期刊论文数量（8）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Inexact alternating direction methods of multipliers for separable convex optimization

可分离凸优化的乘子不精确交替方向法

DOI：
10.1007/s10589-019-00072-2
发表时间：
2019-02-07
期刊：
Computational Optimization and Applications
影响因子：
2.2
作者：
W. Hager;Hongchao Zhang
通讯作者：
Hongchao Zhang

Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System

解决具有非光滑解的最优控制问题的改进Radau配置方法第二部分：成本估计和变换的伴随系统

DOI：
10.1109/cdc.2018.8619426
发表时间：
2018-12-01
期刊：
2018 IEEE Conference on Decision and Control (CDC)
影响因子：
0
作者：
Joseph D. Eide;W. Hager;Anil V. Rao
通讯作者：
Anil V. Rao

Performance Optimization and Guidance of a Low-Altitude Skid-to-Turn Vehicle. Part II: Optimal Guidance

低空滑移转弯车辆的性能优化和制导。

DOI：
10.2514/6.2019-0355
发表时间：
2019-01
期刊：
San Diego
影响因子：
0
作者：
Dennis, Miriam;Rao, Anil V.
通讯作者：
Rao, Anil V.

Convergence rate for a Radau hp collocation method applied to constrained optimal control

应用于约束最优控制的 Radau hp 配置方法的收敛率

DOI：
10.1007/s10589-019-00100-1
发表时间：
2019-05
期刊：
Computational Optimization and Applications
影响因子：
2.2
作者：
Hager, William W.;Hou, Hongyan;Mohapatra, Subhashree;Rao, Anil V.;Wang, Xiang
通讯作者：
Wang, Xiang

Performance Optimization and Guidance of a Low-Altitude Skid-to-Turn Vehicle. Part I: Performance Optimization

低空滑移转弯车辆的性能优化和制导。