{"id":"https://openalex.org/W2343173310","doi":"https://doi.org/10.1007/s10589-019-00103-y","title":"Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning","display_name":"Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning","publication_year":2019,"publication_date":"2019-06-06","ids":{"openalex":"https://openalex.org/W2343173310","doi":"https://doi.org/10.1007/s10589-019-00103-y","mag":"2343173310"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-019-00103-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00103-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00103-y.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00103-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yiran Cui","orcid":"https://orcid.org/0000-0002-4584-4309"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yiran Cui","raw_affiliation_strings":["Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Keiichi Morikuni","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiichi Morikuni","raw_affiliation_strings":["Division of Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-0006, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-0006, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Takashi Tsuchiya","orcid":null},"institutions":[{"id":"https://openalex.org/I116292333","display_name":"National Graduate Institute for Policy Studies","ror":"https://ror.org/03gz5xp73","country_code":"JP","type":"education","lineage":["https://openalex.org/I116292333"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takashi Tsuchiya","raw_affiliation_strings":["National Graduate Institute for Policy Studies, 7-22-1 Roppongi, Minato-ku, Tokyo, 106-8677, Japan"],"affiliations":[{"raw_affiliation_string":"National Graduate Institute for Policy Studies, 7-22-1 Roppongi, Minato-ku, Tokyo, 106-8677, Japan","institution_ids":["https://openalex.org/I116292333"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ken Hayami","orcid":null},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I200475212","display_name":"The Graduate University for Advanced Studies, SOKENDAI","ror":"https://ror.org/0516ah480","country_code":"JP","type":"education","lineage":["https://openalex.org/I200475212"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ken Hayami","raw_affiliation_strings":["National Institute of Informatics and SOKENDAI (The Graduate University for Advanced Studies), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan"],"affiliations":[{"raw_affiliation_string":"National Institute of Informatics and SOKENDAI (The Graduate University for Advanced Studies), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan","institution_ids":["https://openalex.org/I184597095","https://openalex.org/I200475212"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7983,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7352252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"74","issue":"1","first_page":"143","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.7207000255584717,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.7207000255584717,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.225600004196167,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.007300000172108412,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8593999743461609},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6365000009536743},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5645999908447266},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.44350001215934753},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.3953000009059906},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.37310001254081726},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.3626999855041504},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3582000136375427},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.320499986410141}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8593999743461609},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6365000009536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5746999979019165},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5645999908447266},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5212000012397766},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.44350001215934753},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4431999921798706},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38679999113082886},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.3626999855041504},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3582000136375427},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.3203999996185303},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3181000053882599},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.2728999853134155},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.2687000036239624},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.258899986743927}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-019-00103-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00103-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00103-y.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1604.07491","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.07491","pdf_url":"https://arxiv.org/pdf/1604.07491","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:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00103-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-019-00103-y","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":"doi:10.1007/s10589-019-00103-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00103-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00103-y.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1069223013","display_name":null,"funder_award_id":"JSPS KAKENHI","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G186488503","display_name":null,"funder_award_id":"15H02968","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2713586455","display_name":null,"funder_award_id":"15K04768","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3986828568","display_name":null,"funder_award_id":"16K17639","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4227499671","display_name":null,"funder_award_id":"KAKENHI Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4636223006","display_name":null,"funder_award_id":"JSPS KAK","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4827429566","display_name":null,"funder_award_id":"Grant Numbers","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5786340949","display_name":null,"funder_award_id":"KAKENHI Grant Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8430481527","display_name":null,"funder_award_id":"Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2343173310.pdf","grobid_xml":"https://content.openalex.org/works/W2343173310.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W34169854","https://openalex.org/W1506342804","https://openalex.org/W1518039036","https://openalex.org/W1597918674","https://openalex.org/W1961233311","https://openalex.org/W1965256189","https://openalex.org/W1967073510","https://openalex.org/W1968743256","https://openalex.org/W1973207688","https://openalex.org/W1981053712","https://openalex.org/W1981315194","https://openalex.org/W1987953347","https://openalex.org/W1993489874","https://openalex.org/W1996982555","https://openalex.org/W1999913571","https://openalex.org/W2000165536","https://openalex.org/W2006884874","https://openalex.org/W2013945499","https://openalex.org/W2018850201","https://openalex.org/W2019744552","https://openalex.org/W2024978582","https://openalex.org/W2027907985","https://openalex.org/W2030674458","https://openalex.org/W2031735948","https://openalex.org/W2033624514","https://openalex.org/W2035080386","https://openalex.org/W2039400631","https://openalex.org/W2041563548","https://openalex.org/W2043868859","https://openalex.org/W2045721235","https://openalex.org/W2052492400","https://openalex.org/W2054967989","https://openalex.org/W2058696262","https://openalex.org/W2063558363","https://openalex.org/W2065887373","https://openalex.org/W2066459185","https://openalex.org/W2068531154","https://openalex.org/W2071439344","https://openalex.org/W2074316151","https://openalex.org/W2078204800","https://openalex.org/W2083013597","https://openalex.org/W2083229815","https://openalex.org/W2084461590","https://openalex.org/W2085378537","https://openalex.org/W2085548605","https://openalex.org/W2086867325","https://openalex.org/W2093903024","https://openalex.org/W2094435468","https://openalex.org/W2096801802","https://openalex.org/W2101154531","https://openalex.org/W2112502194","https://openalex.org/W2113642685","https://openalex.org/W2118431207","https://openalex.org/W2132894961","https://openalex.org/W2140153041","https://openalex.org/W2149454052","https://openalex.org/W2152309118","https://openalex.org/W2204863336","https://openalex.org/W2284489543","https://openalex.org/W2313084557","https://openalex.org/W2316564661"],"related_works":[],"abstract_inverted_index":{"We":[0],"apply":[1],"novel":[2],"inner-iteration":[3],"preconditioned":[4],"Krylov":[5,43],"subspace":[6,44],"methods":[7,45],"to":[8,26,81],"the":[9,28,36,61,102,127,140,178],"interior-point":[10,40,75,158],"algorithm":[11],"for":[12,149,191],"linear":[13,32],"programming":[14],"(LP).":[15],"Inner-iteration":[16],"preconditioners":[17],"recently":[18],"proposed":[19,78,157],"by":[20],"Morikuni":[21],"and":[22,51,106,139,197],"Hayami":[23],"enable":[24],"us":[25],"overcome":[27],"severe":[29],"ill-conditioning":[30],"of":[31,39,60,70,97,171],"equations":[33],"solved":[34],"in":[35,79,144,165],"final":[37],"phase":[38],"iterations.":[41],"The":[42,111,156,182],"do":[46],"not":[47,65],"suffer":[48],"from":[49,174],"rank-deficiency":[50],"therefore":[52],"no":[53],"preprocessing":[54],"is":[55,77,123],"necessary":[56],"even":[57],"if":[58],"rows":[59],"constraint":[62],"matrix":[63],"are":[64,92],"linearly":[66],"independent.":[67],"By":[68],"means":[69],"these":[71],"methods,":[72],"a":[73,167,186],"new":[74],"recurrence":[76],"order":[80],"omit":[82],"one":[83],"matrix-vector":[84],"product":[85],"at":[86],"each":[87],"step.":[88],"Extensive":[89],"numerical":[90],"experiments":[91],"conducted":[93],"over":[94],"diverse":[95],"instances":[96,173],"140":[98],"LP":[99,172],"problems":[100],"including":[101,195],"Netlib,":[103],"QAPLIB,":[104],"Mittelmann":[105],"Atomizer":[107],"Basis":[108],"Pursuit":[109],"collections.":[110],"largest":[112],"problem":[113],"has":[114],"434,580":[115],"unknowns.":[116],"It":[117],"turns":[118],"out":[119],"that":[120],"our":[121],"implementation":[122],"more":[124],"robust":[125],"than":[126],"standard":[128,179],"public":[129],"domain":[130],"solvers":[131,163,194],"SeDuMi":[132],"(Self-Dual":[133],"Minimization),":[134],"SDPT3":[135],"(Semidefinite":[136],"Programming":[137],"Toh-Todd-T\u00fct\u00fcnc\u00fc)":[138],"LSMR":[141],"iterative":[142,162,198],"solver":[143],"PDCO":[145],"(Primal-Dual":[146],"Barrier":[147],"Method":[148],"Convex":[150],"Objectives)":[151],"without":[152],"increasing":[153],"CPU":[154],"time.":[155],"method":[159],"based":[160],"on":[161],"succeeds":[164],"solving":[166],"fairly":[168,187],"large":[169],"number":[170],"benchmark":[175,189],"libraries":[176],"under":[177],"stopping":[180],"criteria.":[181],"work":[183],"also":[184],"presents":[185],"extensive":[188],"test":[190],"several":[192],"renowned":[193],"direct":[196],"solvers.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}