{"title":"A Gradient Tracking Protocol for Optimization Over Nabla Fractional Multi-Agent Systems","authors":"Shuaiyu Zhou;Yiheng Wei;Shu Liang;Jinde Cao","doi":"10.1109/TSIPN.2024.3402354","DOIUrl":null,"url":null,"abstract":"This paper investigates the distributed consensus optimization over a class of nabla fractional multi-agent systems (nFMASs). The proposed approach, built upon conventional gradient tracking techniques, addresses the specificity of the studied system by introducing a fractional gradient tracking protocol based on globally differential information of optimization variables. This protocol is applicable to nabla fractional systems of any order less than 1 and can be extended to integer discrete-time systems. The distributed optimization algorithms derived from this protocol ensure globally precise convergence under fixed step-sizes, thereby guaranteeing the feasibility of consensus optimization over nFMASs. Simulation results are presented to validate and substantiate the effectiveness of the proposed algorithms.","PeriodicalId":56268,"journal":{"name":"IEEE Transactions on Signal and Information Processing over Networks","volume":"10 ","pages":"500-512"},"PeriodicalIF":3.0000,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Signal and Information Processing over Networks","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10533865/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
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Abstract
This paper investigates the distributed consensus optimization over a class of nabla fractional multi-agent systems (nFMASs). The proposed approach, built upon conventional gradient tracking techniques, addresses the specificity of the studied system by introducing a fractional gradient tracking protocol based on globally differential information of optimization variables. This protocol is applicable to nabla fractional systems of any order less than 1 and can be extended to integer discrete-time systems. The distributed optimization algorithms derived from this protocol ensure globally precise convergence under fixed step-sizes, thereby guaranteeing the feasibility of consensus optimization over nFMASs. Simulation results are presented to validate and substantiate the effectiveness of the proposed algorithms.
期刊介绍：
The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.
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