二阶受限动态优化

Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou
{"title":"二阶受限动态优化","authors":"Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou","doi":"arxiv-2409.11649","DOIUrl":null,"url":null,"abstract":"This paper provides an overview, analysis, and comparison of second-order\ndynamic optimization algorithms, i.e., constrained Differential Dynamic\nProgramming (DDP) and Sequential Quadratic Programming (SQP). Although a\nvariety of these algorithms has been proposed and used successfully, there\nexists a gap in understanding the key differences and advantages, which we aim\nto provide in this work. For constrained DDP, we choose methods that\nincorporate nolinear programming techniques to handle state and control\nconstraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual\nAugmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers.\nBoth DDP and SQP are provided in single- and multiple-shooting formulations,\nwhere constraints that arise from dynamics are encoded implicitly and\nexplicitly, respectively. In addition to reviewing these methods, we propose a\nsingle-shooting PDAL DDP. As a byproduct of the review, we also propose a\nsingle-shooting PDAL DDP which is robust to the growth of penalty parameters\nand performs better than the normal AL variant. We perform extensive numerical\nexperiments on a variety of systems with increasing complexity towards\ninvestigating the quality of the solutions, the levels of constraint violation,\niterations for convergence, and the sensitivity of final solutions with respect\nto initialization. The results show that DDP often has the advantage of finding\nbetter local minima, while SQP tends to achieve better constraint satisfaction.\nFor multiple-shooting formulation, both DDP and SQP can enjoy informed initial\nguesses, while the latter appears to be more advantageous in complex systems.\nIt is also worth highlighting that DDP provides favorable computational\ncomplexity and feedback gains as a byproduct of optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Second-Order Constrained Dynamic Optimization\",\"authors\":\"Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou\",\"doi\":\"arxiv-2409.11649\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper provides an overview, analysis, and comparison of second-order\\ndynamic optimization algorithms, i.e., constrained Differential Dynamic\\nProgramming (DDP) and Sequential Quadratic Programming (SQP). Although a\\nvariety of these algorithms has been proposed and used successfully, there\\nexists a gap in understanding the key differences and advantages, which we aim\\nto provide in this work. For constrained DDP, we choose methods that\\nincorporate nolinear programming techniques to handle state and control\\nconstraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual\\nAugmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers.\\nBoth DDP and SQP are provided in single- and multiple-shooting formulations,\\nwhere constraints that arise from dynamics are encoded implicitly and\\nexplicitly, respectively. In addition to reviewing these methods, we propose a\\nsingle-shooting PDAL DDP. As a byproduct of the review, we also propose a\\nsingle-shooting PDAL DDP which is robust to the growth of penalty parameters\\nand performs better than the normal AL variant. We perform extensive numerical\\nexperiments on a variety of systems with increasing complexity towards\\ninvestigating the quality of the solutions, the levels of constraint violation,\\niterations for convergence, and the sensitivity of final solutions with respect\\nto initialization. The results show that DDP often has the advantage of finding\\nbetter local minima, while SQP tends to achieve better constraint satisfaction.\\nFor multiple-shooting formulation, both DDP and SQP can enjoy informed initial\\nguesses, while the latter appears to be more advantageous in complex systems.\\nIt is also worth highlighting that DDP provides favorable computational\\ncomplexity and feedback gains as a byproduct of optimization.\",\"PeriodicalId\":501286,\"journal\":{\"name\":\"arXiv - MATH - Optimization and Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Optimization and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11649\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Optimization and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11649","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本文概述、分析和比较了二阶动态优化算法,即约束差分动态编程(DDP)和顺序二次编程(SQP)。虽然这些算法的种类繁多,并已被成功提出和使用,但在理解其主要区别和优势方面仍存在差距,我们希望在本研究中提供这方面的信息。对于约束 DDP,我们选择了结合非线性编程技术来处理状态和控制约束的方法,包括增量拉格朗日(AL)、内部点、原始双增量拉格朗日(PDAL)和乘数交替方向法。除了回顾这些方法外,我们还提出了单射 PDAL DDP。作为回顾的副产品,我们还提出了单射 PDAL DDP,它对惩罚参数的增长具有鲁棒性,并且比普通 AL 变体的性能更好。我们在复杂度不断增加的各种系统上进行了大量数值实验,以研究解的质量、违反约束的程度、收敛的迭代次数以及最终解对初始化的敏感性。结果表明,DDP 通常具有找到更好的局部最小值的优势,而 SQP 则倾向于实现更好的约束满足。对于多重射击公式,DDP 和 SQP 都能获得明智的初始猜测,而后者在复杂系统中似乎更具优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Second-Order Constrained Dynamic Optimization
This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these algorithms has been proposed and used successfully, there exists a gap in understanding the key differences and advantages, which we aim to provide in this work. For constrained DDP, we choose methods that incorporate nolinear programming techniques to handle state and control constraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers. Both DDP and SQP are provided in single- and multiple-shooting formulations, where constraints that arise from dynamics are encoded implicitly and explicitly, respectively. In addition to reviewing these methods, we propose a single-shooting PDAL DDP. As a byproduct of the review, we also propose a single-shooting PDAL DDP which is robust to the growth of penalty parameters and performs better than the normal AL variant. We perform extensive numerical experiments on a variety of systems with increasing complexity towards investigating the quality of the solutions, the levels of constraint violation, iterations for convergence, and the sensitivity of final solutions with respect to initialization. The results show that DDP often has the advantage of finding better local minima, while SQP tends to achieve better constraint satisfaction. For multiple-shooting formulation, both DDP and SQP can enjoy informed initial guesses, while the latter appears to be more advantageous in complex systems. It is also worth highlighting that DDP provides favorable computational complexity and feedback gains as a byproduct of optimization.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信