{"id":"https://openalex.org/W4228998417","doi":"https://doi.org/10.1051/ro/2022063","title":"Regularization algorithms for linear copositive problems","display_name":"Regularization algorithms for linear copositive problems","publication_year":2022,"publication_date":"2022-05-01","ids":{"openalex":"https://openalex.org/W4228998417","doi":"https://doi.org/10.1051/ro/2022063"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2022063","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022063","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/03/ro200572.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/03/ro200572.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029454668","display_name":"O. I. Kostyukova","orcid":"https://orcid.org/0000-0002-0959-0831"},"institutions":[{"id":"https://openalex.org/I151823869","display_name":"National Academy of Sciences of Belarus","ror":"https://ror.org/02j8pe645","country_code":"BY","type":"government","lineage":["https://openalex.org/I151823869"]},{"id":"https://openalex.org/I291386647","display_name":"Belarusian State University","ror":"https://ror.org/021036w13","country_code":"BY","type":"education","lineage":["https://openalex.org/I291386647"]},{"id":"https://openalex.org/I4210105280","display_name":"Institute of Mathematics","ror":"https://ror.org/00vsg3p53","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210105280","https://openalex.org/I4210116091"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"Olga I. Kostyukova","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Belarusian State University, Nezavisimosti av. 4, 220030 Minsk, Belarus","Institute of Mathematics, National Academy of Sciences of Belarus, Surganov str. 11, 220072 Minsk, Belarus"],"raw_orcid":"https://orcid.org/0000-0002-0959-0831","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Belarusian State University, Nezavisimosti av. 4, 220030 Minsk, Belarus","institution_ids":["https://openalex.org/I291386647"]},{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Belarus, Surganov str. 11, 220072 Minsk, Belarus","institution_ids":["https://openalex.org/I151823869","https://openalex.org/I4210105280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087817338","display_name":"Tatiana Tchemisova","orcid":"https://orcid.org/0000-0002-2678-2552"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Tatiana V. Tchemisova","raw_affiliation_strings":["Mathematical Department, University of Aveiro, Campus Universit\u00e1rio Santiago, 3810-193 Aveiro, Portugal"],"raw_orcid":"https://orcid.org/0000-0002-2678-2552","affiliations":[{"raw_affiliation_string":"Mathematical Department, University of Aveiro, Campus Universit\u00e1rio Santiago, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07618814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"3","first_page":"1353","last_page":"1371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.8545022010803223},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6304042935371399},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5802440643310547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48215338587760925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45342233777046204},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.4528631865978241},{"id":"https://openalex.org/keywords/proximal-gradient-methods-for-learning","display_name":"Proximal gradient methods for learning","score":0.4436008930206299},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43885260820388794},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4229617118835449},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41743892431259155},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4040212035179138},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.26787662506103516},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1744351089000702},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.17360404133796692},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.1506713330745697},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14978453516960144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06370502710342407}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.8545022010803223},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6304042935371399},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5802440643310547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48215338587760925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45342233777046204},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.4528631865978241},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.4436008930206299},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43885260820388794},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4229617118835449},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41743892431259155},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4040212035179138},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.26787662506103516},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1744351089000702},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.17360404133796692},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.1506713330745697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14978453516960144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06370502710342407},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1051/ro/2022063","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022063","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/03/ro200572.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2022063","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2022063","raw_type":"Text"},{"id":"pmh:oai:elib.bsu.by:123456789/289549","is_oa":true,"landing_page_url":"https://elib.bsu.by/handle/123456789/289549","pdf_url":null,"source":{"id":"https://openalex.org/S4377196361","display_name":"Digital Library of the Belarusian State University (Belarusian State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I291386647","host_organization_name":"Belarusian State University","host_organization_lineage":["https://openalex.org/I291386647"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:numdam.org:RO_2022__56_3_1353_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2022063/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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:ria.ua.pt:10773/36132","is_oa":true,"landing_page_url":"http://hdl.handle.net/10773/36132","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1051/ro/2022063","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022063","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/03/ro200572.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2590986966","display_name":"Center for Research and Development in Mathematics and Applications","funder_award_id":"UIDB/04106/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3069120617","display_name":null,"funder_award_id":"04106","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3119482441","display_name":null,"funder_award_id":"project UIDB/04106/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3461949579","display_name":null,"funder_award_id":"UIDB/04106/2020","funder_id":"https://openalex.org/F4320329951","funder_display_name":"Center for Research and Development in Mathematics and Applications"}],"funders":[{"id":"https://openalex.org/F4320329951","display_name":"Center for Research and Development in Mathematics and Applications","ror":null},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4228998417.pdf","grobid_xml":"https://content.openalex.org/works/W4228998417.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W91728630","https://openalex.org/W1601741115","https://openalex.org/W1964916956","https://openalex.org/W2025776604","https://openalex.org/W2065957732","https://openalex.org/W2080359169","https://openalex.org/W2092569137","https://openalex.org/W2104296611","https://openalex.org/W2120146316","https://openalex.org/W2124487034","https://openalex.org/W2132686144","https://openalex.org/W2140520100","https://openalex.org/W2403050719","https://openalex.org/W2495457432","https://openalex.org/W2745186512","https://openalex.org/W2799712320","https://openalex.org/W3003693830","https://openalex.org/W3130358933","https://openalex.org/W3210125667","https://openalex.org/W4205169475","https://openalex.org/W4236506220","https://openalex.org/W6606511648","https://openalex.org/W6903577126"],"related_works":["https://openalex.org/W1481686068","https://openalex.org/W2164161365","https://openalex.org/W2081588180","https://openalex.org/W2366023887","https://openalex.org/W1943431218","https://openalex.org/W1989857057","https://openalex.org/W2258635466","https://openalex.org/W2034445081","https://openalex.org/W2006280862","https://openalex.org/W51219890"],"abstract_inverted_index":{"The":[0],"paper":[1],"is":[2,26],"devoted":[3],"to":[4,18,66,101],"the":[5,23,30,47,50,58,89,94],"regularization":[6,36,68,107],"of":[7,14,42,49,76,96],"linear":[8,110],"Copositive":[9,111],"Programming":[10,112],"problems":[11,78,98,113],"which":[12],"consists":[13],"transforming":[15],"a":[16,40,72,82],"problem":[17],"an":[19],"equivalent":[20],"form,":[21],"where":[22],"Slater":[24],"condition":[25],"satisfied":[27],"and":[28,45,79,105],"therefore":[29],"strong":[31],"duality":[32],"holds.":[33],"We":[34,86],"describe":[35],"algorithms":[37,63,108],"based":[38,80],"on":[39,46,81],"concept":[41],"immobile":[43],"indices":[44,55],"understanding":[48],"important":[51],"role":[52],"that":[53,88],"these":[54],"play":[56],"in":[57],"feasible":[59],"sets'":[60],"characterization.":[61],"These":[62],"are":[64],"compared":[65],"some":[67],"procedures":[69],"developed":[70],"for":[71,109],"more":[73,103],"general":[74],"case":[75],"convex":[77],"facial":[83],"reduction":[84],"approach.":[85],"show":[87],"immobile-index-based":[90],"approach":[91],"combined":[92],"with":[93],"specifics":[95],"copositive":[97],"allows":[99],"us":[100],"construct":[102],"explicit":[104],"detailed":[106],"than":[114],"those":[115],"already":[116],"available.":[117]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
