{"id":"https://openalex.org/W4414490098","doi":"https://doi.org/10.1007/s10915-025-03041-6","title":"Energy-Stable Swarm-Based Inertial Algorithms for Optimization","display_name":"Energy-Stable Swarm-Based Inertial Algorithms for Optimization","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414490098","doi":"https://doi.org/10.1007/s10915-025-03041-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03041-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-03041-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-025-03041-6.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-025-03041-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074701866","display_name":"Xuelong Gu","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xuelong Gu","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, 29208, SC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, 29208, SC, USA","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035473719","display_name":"Qi Wang","orcid":"https://orcid.org/0000-0001-9928-2703"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qi Wang","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, 29208, SC, USA"],"raw_orcid":"https://orcid.org/0000-0001-9928-2703","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, 29208, SC, USA","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074701866"],"corresponding_institution_ids":["https://openalex.org/I155781252"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13126936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"105","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.8188999891281128},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7692000269889832},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6610999703407288},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6392999887466431},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5166000127792358},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5087000131607056},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.4846000075340271},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4327999949455261},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.41600000858306885}],"concepts":[{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.8188999891281128},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7692000269889832},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6610999703407288},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6392999887466431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6175000071525574},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43059998750686646},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.41600000858306885},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41350001096725464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4104999899864197},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3797000050544739},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3434999883174896},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3319000005722046},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.28999999165534973},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.2572999894618988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03041-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-03041-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-025-03041-6.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-025-03041-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-03041-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-025-03041-6.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5554097790","display_name":null,"funder_award_id":"2242812","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5656541332","display_name":null,"funder_award_id":"DE-SC0025229","funder_id":"https://openalex.org/F4320334545","funder_display_name":"Office of Fossil Energy and Carbon Management"},{"id":"https://openalex.org/G6179455583","display_name":null,"funder_award_id":"DMS-2038080","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6615347451","display_name":null,"funder_award_id":"OIA-2242812","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8921292286","display_name":null,"funder_award_id":"2038080","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320310846","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903"},{"id":"https://openalex.org/F4320334545","display_name":"Office of Fossil Energy and Carbon Management","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4414490098.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1970033879","https://openalex.org/W1988720110","https://openalex.org/W2107941094","https://openalex.org/W2128204029","https://openalex.org/W2152195021","https://openalex.org/W2261462768","https://openalex.org/W2340142742","https://openalex.org/W2796453292","https://openalex.org/W2802568736","https://openalex.org/W2898889412","https://openalex.org/W2914074116","https://openalex.org/W2963333235","https://openalex.org/W2963356890","https://openalex.org/W2963430672","https://openalex.org/W2964580220","https://openalex.org/W2981222369","https://openalex.org/W3105504331","https://openalex.org/W3110766534","https://openalex.org/W3153588574","https://openalex.org/W3159813613","https://openalex.org/W3188492639","https://openalex.org/W4301014524","https://openalex.org/W4302422232","https://openalex.org/W4385772956","https://openalex.org/W4392356011","https://openalex.org/W4405110434","https://openalex.org/W4405475068","https://openalex.org/W4410109186"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1],"formulate":[2],"the":[3,27,58,68,72,74,79,85,89,93,99,102],"swarming":[4],"optimization":[5],"problem":[6],"as":[7],"a":[8,16,50,118],"weakly":[9],"coupled,":[10],"dissipative":[11],"dynamical":[12,59],"system":[13,60,75],"governed":[14],"by":[15,84],"controlled":[17],"energy":[18,65],"dissipation":[19,66],"rate":[20],"and":[21,37],"initial":[22],"velocities":[23],"that":[24,61],"adhere":[25],"to":[26],"nonequilibrium":[28],"Onsager":[29],"principle.":[30],"In":[31],"this":[32],"formulation,":[33],"agents\u2019":[34],"inertia,":[35],"positions,":[36],"masses":[38],"are":[39],"dynamically":[40],"coupled.":[41],"To":[42],"enable":[43],"rapid":[44],"convergence":[45],"toward":[46],"equilibrium,":[47,73],"we":[48],"develop":[49],"class":[51],"of":[52,78,91,101,121],"efficient,":[53],"energy-stable":[54],"numerical":[55],"algorithms":[56],"for":[57],"preserve":[62],"or":[63],"enhance":[64],"at":[67],"discrete":[69],"level.":[70],"At":[71],"reaches":[76],"one":[77],"lowest":[80],"local":[81],"minima":[82],"explored":[83],"agents,":[86],"thereby":[87],"improving":[88],"likelihood":[90],"identifying":[92],"global":[94],"minimum.":[95],"Numerical":[96],"experiments":[97],"confirm":[98],"effectiveness":[100],"proposed":[103],"approach,":[104],"demonstrating":[105],"significant":[106],"advantages":[107],"over":[108],"traditional":[109],"swarm-based":[110],"gradient":[111],"descent":[112],"methods,":[113],"especially":[114],"when":[115],"operating":[116],"with":[117],"limited":[119],"number":[120],"agents.":[122]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}
