{"id":"https://openalex.org/W2948172096","doi":"https://doi.org/10.1007/s10957-021-01820-3","title":"Quartic First-Order Methods for Low-Rank Minimization","display_name":"Quartic First-Order Methods for Low-Rank Minimization","publication_year":2021,"publication_date":"2021-03-23","ids":{"openalex":"https://openalex.org/W2948172096","doi":"https://doi.org/10.1007/s10957-021-01820-3","mag":"2948172096"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-021-01820-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-021-01820-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.10791","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Radu-Alexandru Dragomir","orcid":"https://orcid.org/0000-0002-4600-7748"},"institutions":[{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Radu-Alexandru Dragomir","raw_affiliation_strings":["Universit\u00e9 Toulouse 1 Capitole & D.I. \u00c9cole Normale Sup\u00e9rieure, Paris, France"],"raw_orcid":"https://orcid.org/0000-0002-4600-7748","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Toulouse 1 Capitole & D.I. \u00c9cole Normale Sup\u00e9rieure, Paris, France","institution_ids":["https://openalex.org/I3131550300"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alexandre d\u2019Aspremont","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre d\u2019Aspremont","raw_affiliation_strings":["CNRS & D.I. \u00c9cole Normale Sup\u00e9rieure, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS & D.I. \u00c9cole Normale Sup\u00e9rieure, Paris, France","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":null,"display_name":"J\u00e9r\u00f4me Bolte","orcid":null},"institutions":[{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Bolte","raw_affiliation_strings":["Universit\u00e9 Toulouse 1 Capitole, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Toulouse 1 Capitole, Toulouse, France","institution_ids":["https://openalex.org/I3131550300"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3131550300"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6995,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.74940991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"189","issue":"2","first_page":"341","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8094000220298767,"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":0.8094000220298767,"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":0.12030000239610672,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0414000004529953,"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/quartic-function","display_name":"Quartic function","score":0.6237000226974487},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6018000245094299},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5202999711036682},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4729999899864197},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.4203999936580658},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4036000072956085},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.38100001215934753},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.37560001015663147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8492000102996826},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.6237000226974487},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6018000245094299},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5202999711036682},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4729999899864197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4505999982357025},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3653999865055084},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3522999882698059},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.31139999628067017},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C117139701","wikidata":"https://www.wikidata.org/wiki/Q7269363","display_name":"Quartic surface","level":3,"score":0.251800000667572},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-021-01820-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-021-01820-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.10791","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.10791","pdf_url":"https://arxiv.org/pdf/1901.10791","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:RePEc:spr:joptap:v:189:y:2021:i:2:d:10.1007_s10957-021-01820-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-021-01820-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1901.10791","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.10791","pdf_url":"https://arxiv.org/pdf/1901.10791","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G3781033834","display_name":null,"funder_award_id":"FA9550-19-1-7026","funder_id":"https://openalex.org/F4320337525","funder_display_name":"Air Force Materiel Command"},{"id":"https://openalex.org/G5838787665","display_name":"PaRis Artificial Intelligence Research InstitutE","funder_award_id":"ANR-19-P3IA-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G978446787","display_name":null,"funder_award_id":"FA9550-18-1-0226","funder_id":"https://openalex.org/F4320337525","funder_display_name":"Air Force Materiel Command"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320337525","display_name":"Air Force Materiel Command","ror":"https://ror.org/006gmme17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1534112425","https://openalex.org/W1836708065","https://openalex.org/W1898843043","https://openalex.org/W1981276685","https://openalex.org/W1986891697","https://openalex.org/W1989291446","https://openalex.org/W2021361347","https://openalex.org/W2023059467","https://openalex.org/W2034632843","https://openalex.org/W2067931421","https://openalex.org/W2093492509","https://openalex.org/W2103972604","https://openalex.org/W2106005123","https://openalex.org/W2110096996","https://openalex.org/W2112104211","https://openalex.org/W2118550318","https://openalex.org/W2120575449","https://openalex.org/W2138505091","https://openalex.org/W2142949395","https://openalex.org/W2150386905","https://openalex.org/W2168084958","https://openalex.org/W2169658215","https://openalex.org/W2229285313","https://openalex.org/W2535496140","https://openalex.org/W2551153860","https://openalex.org/W2566608758","https://openalex.org/W2571268788","https://openalex.org/W2611328865","https://openalex.org/W2962706047","https://openalex.org/W2963967579","https://openalex.org/W4200346838","https://openalex.org/W6600002382","https://openalex.org/W6600236328"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2019-06-14T00:00:00"}