{"id":"https://openalex.org/W3085330744","doi":"https://doi.org/10.1137/20m1333316","title":"Newton-like Inertial Dynamics and Proximal Algorithms Governed by Maximally Monotone Operators","display_name":"Newton-like Inertial Dynamics and Proximal Algorithms Governed by Maximally Monotone Operators","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3085330744","doi":"https://doi.org/10.1137/20m1333316","mag":"3085330744"},"language":"en","primary_location":{"id":"doi:10.1137/20m1333316","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1333316","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038818485","display_name":"H\u00e9dy Attouch","orcid":"https://orcid.org/0000-0003-2676-0887"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hedy Attouch","raw_affiliation_strings":["Institut Montpelli\u00e9rain Alexander Grothendieck"],"affiliations":[{"raw_affiliation_string":"Institut Montpelli\u00e9rain Alexander Grothendieck","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014647378","display_name":"Szil\u00e1rd Csaba L\u00e1szl\u00f3","orcid":"https://orcid.org/0000-0001-5140-1144"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Szil\u00e1rd Csaba L\u00e1szl\u00f3","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038818485"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.518,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94120681,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"4","first_page":"3252","last_page":"3283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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":0.9991999864578247,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8144017457962036},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7286323308944702},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7245649099349976},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6477159261703491},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5635151863098145},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5172553658485413},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5082097053527832},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.50689297914505},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4994068145751953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4969959557056427},{"id":"https://openalex.org/keywords/proximal-gradient-methods-for-learning","display_name":"Proximal gradient methods for learning","score":0.47979336977005005},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4637506604194641},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4608250856399536},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.44573190808296204},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.4443676769733429},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.41529133915901184},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.41018858551979065},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3883504867553711},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3805055618286133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3410460650920868},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.328180730342865},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.12008222937583923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10613670945167542},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08510494232177734}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8144017457962036},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7286323308944702},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7245649099349976},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6477159261703491},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5635151863098145},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5172553658485413},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5082097053527832},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.50689297914505},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4994068145751953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4969959557056427},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.47979336977005005},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4637506604194641},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4608250856399536},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.44573190808296204},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4443676769733429},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41529133915901184},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.41018858551979065},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3883504867553711},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3805055618286133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3410460650920868},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.328180730342865},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.12008222937583923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10613670945167542},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08510494232177734},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1333316","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1333316","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8505300529","display_name":null,"funder_award_id":"CA16228","funder_id":"https://openalex.org/F4320320366","funder_display_name":"European Cooperation in Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320366","display_name":"European Cooperation in Science and Technology","ror":"https://ror.org/01bstzn19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W84725740","https://openalex.org/W146900863","https://openalex.org/W199410564","https://openalex.org/W322738573","https://openalex.org/W1837565340","https://openalex.org/W1974485522","https://openalex.org/W1989464734","https://openalex.org/W2038497950","https://openalex.org/W2062016584","https://openalex.org/W2075803640","https://openalex.org/W2095980290","https://openalex.org/W2104311270","https://openalex.org/W2302721240","https://openalex.org/W2528062157","https://openalex.org/W2599455075","https://openalex.org/W2605652624","https://openalex.org/W2612442615","https://openalex.org/W2731666329","https://openalex.org/W2759432802","https://openalex.org/W2788242395","https://openalex.org/W2800783024","https://openalex.org/W2921509219","https://openalex.org/W2963237896","https://openalex.org/W2963505547","https://openalex.org/W2963804953","https://openalex.org/W2964018031","https://openalex.org/W2964216752","https://openalex.org/W2987364857","https://openalex.org/W2996459728","https://openalex.org/W3027891624","https://openalex.org/W3099827691","https://openalex.org/W3100706439","https://openalex.org/W3123649567","https://openalex.org/W3156246676"],"related_works":["https://openalex.org/W3208916810","https://openalex.org/W1995757014","https://openalex.org/W3009102021","https://openalex.org/W2570633406","https://openalex.org/W4287828482","https://openalex.org/W2972356172","https://openalex.org/W4292651679","https://openalex.org/W2062184313","https://openalex.org/W2011881806","https://openalex.org/W2088624648"],"abstract_inverted_index":{"The":[0],"introduction":[1],"of":[2,10,70,84,93,112,119],"the":[3,7,24,35,42,56,71,81,85,90,94,108,113,116,120],"Hessian":[4],"damping":[5],"in":[6],"continuous":[8],"version":[9],"Nesterov's":[11],"accelerated":[12],"gradient":[13,21],"method":[14],"provides,":[15],"by":[16,45,62],"temporal":[17],"discretization,":[18],"fast":[19],"proximal":[20],"algorithms":[22,102],"where":[23,55],"oscillations":[25],"are":[26],"significantly":[27],"attenuated.":[28],"We":[29,39],"will":[30],"extend":[31],"these":[32,101],"results":[33],"to":[34,87,97,103],"maximally":[36,57],"monotone":[37,58],"case.":[38],"rely":[40],"on":[41],"technique":[43],"introduced":[44],"Attouch":[46],"and":[47,89,115],"Peypouquet":[48],"[Math.":[49],"Program.,":[50],"174":[51],"(2019),":[52],"pp.":[53],"391--432],":[54],"operator":[59],"is":[60],"replaced":[61],"its":[63],"Yosida":[64],"approximation":[65],"with":[66],"an":[67],"appropriate":[68],"adjustment":[69],"regularization":[72],"parameter.":[73],"In":[74],"a":[75],"general":[76],"Hilbert":[77],"framework,":[78],"we":[79,106],"obtain":[80,107],"weak":[82],"convergence":[83,92,109,118],"iterates":[86],"equilibria,":[88],"rapid":[91,117],"discrete":[95],"velocities":[96],"zero.":[98,123],"By":[99],"specializing":[100],"convex":[104],"minimization,":[105],"rate":[110],"$o(1/k^2)$":[111],"values,":[114],"gradients":[121],"toward":[122]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}