Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism
In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. Firstly, the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are li...
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| Veröffentlicht in: | Journal of systems science and complexity 2023-10, Vol.36 (5), p.1927-1948 |
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| container_end_page | 1948 |
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| container_issue | 5 |
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| container_title | Journal of systems science and complexity |
| container_volume | 36 |
| creator | Lu, Jiajie Wang, Yong Fan, Yuan |
| description | In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. Firstly, the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked. Based on this result, a fractional order iteration approach has been developed by modelling the system with fractional order dynamics. Secondly, to reduce the comsumption of computation, a feedback based event-triggered mechanism has been introduced to the gradient descent method. The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method, and Zeno behavior is proved to be avoided simultaneously. Lastly, the effectiveness and advantages of the proposed algorithms are verified by numerical simulations. |
| doi_str_mv | 10.1007/s11424-023-2028-9 |
| format | Article |
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Lastly, the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.</description><subject>Algorithms</subject><subject>Complex Systems</subject><subject>Control</subject><subject>Convergence</subject><subject>Dynamic stability</subject><subject>Integers</subject><subject>Iterative methods</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Statistics</subject><subject>Systems Theory</subject><issn>1009-6124</issn><issn>1559-7067</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kDFPwzAUhC0EEqXwA9giMRv8XhzHHqG0pVKrLmVgshzHaVO1SbFTJP49joLExHRPp-9OekfIPbBHYCx_CgAcOWWYUmQoqbogI8gyRXMm8st4M6aoAOTX5CaEPWOpUEyOyMfMG9vVbWMOydqXzieLznnTO0nV-mTuTVm7pkteXbC9rly3a8vkxQRXJhGafkWXbny93TofrZWzO9PU4XhLripzCO7uV8fkfTbdTN7ocj1fTJ6X1KKQHXXAeWZ5ClxKnipXAgKzCNbIShaigKJQKVRZLmRmENPSWDC5FbawpsAC0zF5GHpPvv08u9DpfXv28Z-gUeYKcoVcRAoGyvo2BO8qffL10fhvDUz3C-phQR0X1P2CWsUMDpkQ2Sa-99f8f-gH5kVzHA</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Lu, Jiajie</creator><creator>Wang, Yong</creator><creator>Fan, Yuan</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism</title><author>Lu, Jiajie ; Wang, Yong ; Fan, Yuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-e1445c431488439ed1210c21ca8f8b6b1bb931f57685a223dac1a7c6cbcab2b23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Complex Systems</topic><topic>Control</topic><topic>Convergence</topic><topic>Dynamic stability</topic><topic>Integers</topic><topic>Iterative methods</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Statistics</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lu, Jiajie</creatorcontrib><creatorcontrib>Wang, Yong</creatorcontrib><creatorcontrib>Fan, Yuan</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of systems science and complexity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lu, Jiajie</au><au>Wang, Yong</au><au>Fan, Yuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism</atitle><jtitle>Journal of systems science and complexity</jtitle><stitle>J Syst Sci Complex</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>36</volume><issue>5</issue><spage>1927</spage><epage>1948</epage><pages>1927-1948</pages><issn>1009-6124</issn><eissn>1559-7067</eissn><abstract>In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. 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| subjects | Algorithms Complex Systems Control Convergence Dynamic stability Integers Iterative methods Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Operations Research/Decision Theory Optimization Statistics Systems Theory |
| title | Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism |
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