{"id":"https://openalex.org/W7204470331","doi":"https://doi.org/10.48550/arxiv.2608.25312","title":"Accelerated Gradient Flow with Endogenous Gradient-Memory Anchor: Selection and Restoring Damping","display_name":"Accelerated Gradient Flow with Endogenous Gradient-Memory Anchor: Selection and Restoring Damping","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204470331","doi":"https://doi.org/10.48550/arxiv.2608.25312"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2608.25312","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25312","pdf_url":"https://arxiv.org/pdf/2608.25312","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.25312","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075880045","display_name":"Chinedu Izuchukwu","orcid":"https://orcid.org/0000-0002-8262-8605","observed_orcids":["https://orcid.org/0000-0002-8262-8605"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Izuchukwu, Chinedu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148471046","display_name":"Ernest Obini","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Obini, Ernest","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148412404","display_name":"Jen-Chih Yao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao, Jen-Chih","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028260946","display_name":"Shengda Zeng","orcid":"https://orcid.org/0000-0003-1818-842X","observed_orcids":["https://orcid.org/0000-0003-1818-842X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Shengda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7411999702453613,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7411999702453613,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.16349999606609344,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.030400000512599945,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/first-order-methods","display_name":"first-order methods","score":0.7039999961853027},{"id":"https://openalex.org/keywords/global-existence-and-uniqueness","display_name":"global existence and uniqueness","score":0.7730000019073486},{"id":"https://openalex.org/keywords/lyapunov-analysis","display_name":"Lyapunov analysis","score":0.9179999828338623},{"id":"https://openalex.org/keywords/polynomial-decay","display_name":"polynomial decay","score":0.6629999876022339},{"id":"https://openalex.org/keywords/dissipative-dynamics","display_name":"dissipative dynamics","score":0.453000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.717199981212616},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6740999817848206},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5565000176429749},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.526199996471405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49410000443458557},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.489300012588501},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4828000068664551},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.41760000586509705},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2773999869823456}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.25312","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25312","pdf_url":"https://arxiv.org/pdf/2608.25312","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.25312","doi":"https://doi.org/10.48550/arxiv.2608.25312","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.25312","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.25312","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25312","pdf_url":"https://arxiv.org/pdf/2608.25312","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204470331.pdf","grobid_xml":"https://content.openalex.org/works/W7204470331.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,139],"introduce":[1],"an":[2,7,169,178],"accelerated":[3,75,188],"gradient":[4],"flow":[5],"with":[6,79],"endogenous":[8],"gradient-memory":[9],"anchor":[10,17,120,167],"and":[11,51,65,191],"a":[12,20,96,142],"nonlinear":[13,28,81,156],"restoring--damping":[14,82,192],"feedback.":[15],"The":[16,40],"evolves":[18],"from":[19,37,47,165],"weighted":[21,144],"history":[22],"of":[23,67,117],"the":[24,27,33,38,48,74,80,90,101,107,113,118,130,133,148,155,161,166,172,186],"gradients,":[25],"while":[26],"feedback":[29,157],"is":[30,105,109,158],"modulated":[31],"by":[32],"squared":[34],"coordinatewise":[35],"displacement":[36],"anchor.":[39],"resulting":[41],"dynamics":[42,131,176],"uses":[43],"only":[44],"first-order":[45],"information":[46],"objective":[49],"function":[50],"does":[52],"not":[53],"involve":[54],"explicit":[55],"Hessian":[56],"information.":[57],"Under":[58,87],"suitable":[59],"assumptions,":[60,89],"we":[61],"establish":[62,141],"global":[63],"existence":[64],"uniqueness":[66],"strong":[68],"solutions.":[69],"A":[70],"Lyapunov":[71],"analysis":[72],"yields":[73],"objective-value":[76,189],"estimate":[77,146],"$F(x(t))-F^\\star=\\mathcal{O}(t^{-2})$,":[78],"term":[83],"contributing":[84],"additional":[85,179],"dissipation.":[86],"similar":[88],"primal":[91],"trajectory":[92,162],"converges":[93],"strongly":[94],"to":[95,137],"minimizer.":[97],"When,":[98],"in":[99,152],"addition,":[100],"solution":[102,135],"set":[103],"$S$":[104],"affine,":[106],"limit":[108],"identified":[110],"explicitly":[111],"as":[112],"Euclidean":[114],"projection":[115],"$P_S(z_0)$":[116],"initial":[119],"$z_0$":[121],"onto":[122],"$S$.":[123],"In":[124],"particular,":[125],"for":[126,147],"rank-deficient":[127],"least-squares":[128,134],"problems,":[129],"selects":[132],"closest":[136],"$z_0$.":[138],"also":[140],"finite":[143],"dissipation":[145],"phase":[149,175],"variable.":[150],"Moreover,":[151],"coordinates":[153],"where":[154],"active,":[159],"if":[160],"remains":[163],"separated":[164],"over":[168],"interval,":[170],"then":[171],"corresponding":[173],"homogeneous":[174],"acquires":[177],"polynomial":[180],"decay":[181],"factor.":[182],"Numerical":[183],"experiments":[184],"illustrate":[185],"minimizer-selection,":[187],"decay,":[190],"mechanisms.":[193]},"counts_by_year":[],"updated_date":"2026-08-30T07:30:35.949966","created_date":"2026-08-28T00:00:00"}
