{"title":"分布式时变优化的无hessian固定/预定义时间算法","authors":"Zeng-Di Zhou;Ge Guo;Renyongkang Zhang","doi":"10.1109/TSMC.2025.3593476","DOIUrl":null,"url":null,"abstract":"This article proposes distributed algorithms free of Hessian for both time-invariant and time-varying optimization (TVO) problems. To this end, a subsystem is introduced to estimate the system’s gradient-sum in a distributed average tracking manner, based on which a distributed protocol is designed by coupling the gradient-sum descent method and state consensus scheme. Additionally, in our TVO method, a norm-normalized signum function is introduced to compensate for the internal drift of the system using its discontinuity. These methods are interesting as they can achieve the optimization goal within a specific time independent of system’s initial states, i.e., satisfy fixed-/predefined-time convergence. Moreover, a fully distributed adaptive gain method is proposed to avoid obtaining some global information. The numerical simulation and case study are provided to corroborate the effectiveness of proposed algorithms.","PeriodicalId":48915,"journal":{"name":"IEEE Transactions on Systems Man Cybernetics-Systems","volume":"55 10","pages":"6890-6900"},"PeriodicalIF":8.7000,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hessian-Free Fixed-/Predefined-Time Algorithms for Distributed Time-Varying Optimization\",\"authors\":\"Zeng-Di Zhou;Ge Guo;Renyongkang Zhang\",\"doi\":\"10.1109/TSMC.2025.3593476\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article proposes distributed algorithms free of Hessian for both time-invariant and time-varying optimization (TVO) problems. To this end, a subsystem is introduced to estimate the system’s gradient-sum in a distributed average tracking manner, based on which a distributed protocol is designed by coupling the gradient-sum descent method and state consensus scheme. Additionally, in our TVO method, a norm-normalized signum function is introduced to compensate for the internal drift of the system using its discontinuity. These methods are interesting as they can achieve the optimization goal within a specific time independent of system’s initial states, i.e., satisfy fixed-/predefined-time convergence. Moreover, a fully distributed adaptive gain method is proposed to avoid obtaining some global information. The numerical simulation and case study are provided to corroborate the effectiveness of proposed algorithms.\",\"PeriodicalId\":48915,\"journal\":{\"name\":\"IEEE Transactions on Systems Man Cybernetics-Systems\",\"volume\":\"55 10\",\"pages\":\"6890-6900\"},\"PeriodicalIF\":8.7000,\"publicationDate\":\"2025-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Systems Man Cybernetics-Systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/11124556/\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Systems Man Cybernetics-Systems","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/11124556/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Hessian-Free Fixed-/Predefined-Time Algorithms for Distributed Time-Varying Optimization
This article proposes distributed algorithms free of Hessian for both time-invariant and time-varying optimization (TVO) problems. To this end, a subsystem is introduced to estimate the system’s gradient-sum in a distributed average tracking manner, based on which a distributed protocol is designed by coupling the gradient-sum descent method and state consensus scheme. Additionally, in our TVO method, a norm-normalized signum function is introduced to compensate for the internal drift of the system using its discontinuity. These methods are interesting as they can achieve the optimization goal within a specific time independent of system’s initial states, i.e., satisfy fixed-/predefined-time convergence. Moreover, a fully distributed adaptive gain method is proposed to avoid obtaining some global information. The numerical simulation and case study are provided to corroborate the effectiveness of proposed algorithms.
期刊介绍:
The IEEE Transactions on Systems, Man, and Cybernetics: Systems encompasses the fields of systems engineering, covering issue formulation, analysis, and modeling throughout the systems engineering lifecycle phases. It addresses decision-making, issue interpretation, systems management, processes, and various methods such as optimization, modeling, and simulation in the development and deployment of large systems.