{"id":"https://openalex.org/W3170011685","doi":"https://doi.org/10.1090/mcom/3802","title":"LSOS: Line-search second-order stochastic optimization methods for nonconvex finite sums","display_name":"LSOS: Line-search second-order stochastic optimization methods for nonconvex finite sums","publication_year":2022,"publication_date":"2022-11-30","ids":{"openalex":"https://openalex.org/W3170011685","doi":"https://doi.org/10.1090/mcom/3802","mag":"3170011685"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3802","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3802","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5044144663","display_name":"Daniela di Serafino","orcid":"https://orcid.org/0000-0001-8215-0771"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Daniela di Serafino","raw_affiliation_strings":["Department of Mathematics and Applications \u00e2\u0080\u009cRenato Caccioppoli\u00e2\u0080\u009d, University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy","Department of Mathematics and Applications \"Renato Caccioppoli\", University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications \u00e2\u0080\u009cRenato Caccioppoli\u00e2\u0080\u009d, University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy","institution_ids":["https://openalex.org/I71267560"]},{"raw_affiliation_string":"Department of Mathematics and Applications \"Renato Caccioppoli\", University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029757006","display_name":"Nata\u0161a Kreji\u0107","orcid":"https://orcid.org/0000-0003-3348-7233"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Nata\u0161a Kreji\u0107","raw_affiliation_strings":["Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 4, 21000 Novi Sad, Serbia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 4, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023718232","display_name":"Nata\u0161a Krklec Jerinki\u0107","orcid":"https://orcid.org/0000-0001-5195-9295"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Nata\u0161a Krklec Jerinki\u0107","raw_affiliation_strings":["Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 4, 21000 Novi Sad, Serbia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 4, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075999000","display_name":"Marco Viola","orcid":"https://orcid.org/0000-0002-2140-8094"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Viola","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u00e2\u0080\u009cLuigi Vanvitelli\u00e2\u0080\u009d, Viale A. Lincoln 5, 81100 Caserta, Italy","Department of Mathematics and Physics, University of Campania \"Luigi Vanvitelli\", Viale A. Lincoln 5, 81100 Caserta, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u00e2\u0080\u009cLuigi Vanvitelli\u00e2\u0080\u009d, Viale A. Lincoln 5, 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \"Luigi Vanvitelli\", Viale A. Lincoln 5, 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044144663"],"corresponding_institution_ids":["https://openalex.org/I71267560"],"apc_list":null,"apc_paid":null,"fwci":1.5908,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.85188361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"92","issue":"341","first_page":"1273","last_page":"1299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":1.0,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":1.0,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.8121814727783203},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7456359267234802},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7069425582885742},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6885297298431396},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6227051615715027},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5576267838478088},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5376374125480652},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5342836380004883},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5308821201324463},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49991726875305176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.429002046585083},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.41360437870025635},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.39721935987472534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13353610038757324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12946093082427979}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8121814727783203},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7456359267234802},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7069425582885742},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6885297298431396},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6227051615715027},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5576267838478088},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5376374125480652},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5342836380004883},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5308821201324463},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49991726875305176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.429002046585083},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41360437870025635},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39721935987472534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13353610038757324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12946093082427979},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3802","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3802","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325777","display_name":"Universit\u00e0 degli Studi della Campania Luigi Vanvitelli","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W391985582","https://openalex.org/W1577337550","https://openalex.org/W1592294486","https://openalex.org/W1614009013","https://openalex.org/W1707676469","https://openalex.org/W1983911994","https://openalex.org/W1991083751","https://openalex.org/W1994616650","https://openalex.org/W2042173174","https://openalex.org/W2061570747","https://openalex.org/W2070709745","https://openalex.org/W2098478073","https://openalex.org/W2106036238","https://openalex.org/W2107438106","https://openalex.org/W2179354704","https://openalex.org/W2524032428","https://openalex.org/W2587483164","https://openalex.org/W2738488603","https://openalex.org/W2798461040","https://openalex.org/W2799870997","https://openalex.org/W2804009132","https://openalex.org/W2804140211","https://openalex.org/W2900493964","https://openalex.org/W2909947102","https://openalex.org/W2952215077","https://openalex.org/W2954160693","https://openalex.org/W2962936775","https://openalex.org/W2963397933","https://openalex.org/W2963433607","https://openalex.org/W2963813563","https://openalex.org/W2963941964","https://openalex.org/W2963952517","https://openalex.org/W2964303576","https://openalex.org/W2970227300","https://openalex.org/W2979411530","https://openalex.org/W2983582984","https://openalex.org/W2990754067","https://openalex.org/W2997241048","https://openalex.org/W2997265885","https://openalex.org/W3005484777","https://openalex.org/W3006477280","https://openalex.org/W3023674141","https://openalex.org/W3025544109","https://openalex.org/W3030916542","https://openalex.org/W3080939493","https://openalex.org/W3110179172","https://openalex.org/W3158421934","https://openalex.org/W3173141421","https://openalex.org/W4232171345"],"related_works":["https://openalex.org/W1677518548","https://openalex.org/W4286857066","https://openalex.org/W3213958552","https://openalex.org/W4243698225","https://openalex.org/W4238239967","https://openalex.org/W4297812081","https://openalex.org/W2949926331","https://openalex.org/W2754545762","https://openalex.org/W4299562540","https://openalex.org/W3175273680"],"abstract_inverted_index":{"We":[0,11],"develop":[1],"a":[2,51],"line-search":[3,67],"second-order":[4],"algorithmic":[5],"framework":[6,38],"for":[7],"minimizing":[8],"finite":[9],"sums.":[10],"do":[12],"not":[13],"make":[14],"any":[15],"convexity":[16],"assumptions,":[17],"but":[18],"require":[19],"the":[20,23,62,66,76,83,88,92,96,112],"terms":[21],"of":[22,70,82,85,114],"sum":[24],"to":[25,60,87],"be":[26],"continuously":[27],"differentiable":[28],"and":[29,42],"have":[30],"Lipschitz-continuous":[31],"gradients.":[32],"The":[33],"methods":[34],"fitting":[35],"into":[36],"this":[37],"combine":[39],"line":[40],"searches":[41],"suitably":[43],"decaying":[44],"step":[45],"lengths.":[46],"A":[47],"key":[48],"issue":[49],"is":[50,73],"two-step":[52],"sampling":[53],"at":[54],"each":[55],"iteration,":[56],"which":[57],"allows":[58],"us":[59],"control":[61],"error":[63],"present":[64],"in":[65,75],"procedure.":[68],"Stationarity":[69],"limit":[71],"points":[72],"proved":[74],"almost-sure":[77,80],"sense,":[78],"while":[79],"convergence":[81],"sequence":[84],"approximations":[86],"solution":[89],"holds":[90],"with":[91,105],"additional":[93],"hypothesis":[94],"that":[95],"functions":[97],"are":[98],"strongly":[99],"convex.":[100],"Numerical":[101],"experiments,":[102],"including":[103],"comparisons":[104],"state-of-the":[106],"art":[107],"stochastic":[108],"optimization":[109],"methods,":[110],"show":[111],"efficiency":[113],"our":[115],"approach.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}