{"id":"https://openalex.org/W4405276262","doi":"https://doi.org/10.1137/24m1716288","title":"A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure","display_name":"A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure","publication_year":2026,"publication_date":"2026-05-21","ids":{"openalex":"https://openalex.org/W4405276262","doi":"https://doi.org/10.1137/24m1716288"},"language":"en","primary_location":{"id":"doi:10.1137/24m1716288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1716288","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2412.07731","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082384721","display_name":"Nils-Christian Kempke","orcid":"https://orcid.org/0000-0003-4492-9818"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nils\u2013Christian Kempke","raw_affiliation_strings":["Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005949084","display_name":"Daniel Rehfeldt","orcid":"https://orcid.org/0000-0002-2877-074X"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I4210138807","display_name":"IVU Traffic Technologies (Germany)","ror":"https://ror.org/04r2khh81","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210138807"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Rehfeldt","raw_affiliation_strings":["Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","IVU Traffic Technologies, Bundesallee 88, 12161 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"IVU Traffic Technologies, Bundesallee 88, 12161 Berlin, Germany","institution_ids":["https://openalex.org/I4210138807"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066794150","display_name":"Thorsten Koch","orcid":"https://orcid.org/0000-0002-1967-0077"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thorsten Koch","raw_affiliation_strings":["Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","Chair of Software and Algorithms for Discrete Optimization, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni\u00a0136, 10623, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Chair of Software and Algorithms for Discrete Optimization, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni\u00a0136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.03268641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"3","first_page":"B360","last_page":"B385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9884999990463257,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9884999990463257,"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/T12810","display_name":"Real-time simulation and control systems","score":0.9871000051498413,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9819999933242798,"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/massively-parallel","display_name":"Massively parallel","score":0.6802924871444702},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6091179847717285},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4664914608001709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4553326964378357},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4479489028453827},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3172905445098877},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21031233668327332},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20313161611557007}],"concepts":[{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.6802924871444702},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6091179847717285},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4664914608001709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4553326964378357},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4479489028453827},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3172905445098877},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21031233668327332},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20313161611557007}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/24m1716288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1716288","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2412.07731","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.07731","pdf_url":"https://arxiv.org/pdf/2412.07731","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2412.07731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2412.07731","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2412.07731","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.07731","pdf_url":"https://arxiv.org/pdf/2412.07731","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323803","display_name":"Bundesministerium f\u00fcr Wirtschaft und Energie","ror":"https://ror.org/02vgg2808"},{"id":"https://openalex.org/F4320331625","display_name":"Gauss Centre for Supercomputing","ror":"https://ror.org/0585fsj26"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4405276262.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2023839151","https://openalex.org/W1774183074","https://openalex.org/W2057488824","https://openalex.org/W2334687145","https://openalex.org/W2178011914","https://openalex.org/W4235962491","https://openalex.org/W2061778832","https://openalex.org/W1513001507","https://openalex.org/W2257153718","https://openalex.org/W3134702077"],"abstract_inverted_index":{"In":[0],"practice,":[1],"non-specialized":[2],"interior":[3],"point":[4],"algorithms":[5],"often":[6],"cannot":[7],"utilize":[8],"the":[9,48,75,84,98,112,122,128,142],"massively":[10],"parallel":[11,49],"compute":[12,20],"resources":[13],"offered":[14],"by":[15,135],"modern":[16],"many-":[17],"and":[18,96,108],"multi-core":[19],"platforms.":[21],"However,":[22],"efficient":[23],"distributed":[24],"solution":[25],"techniques":[26],"are":[27],"required,":[28],"especially":[29],"for":[30,41,105],"large-scale":[31,136,152],"linear":[32,44,76,99],"programs.":[33],"This":[34,70],"article":[35],"describes":[36],"a":[37,56,64,89,148],"new":[38],"decomposition":[39,93,119],"technique":[40],"systems":[42,78],"of":[43,83,114,144,150,155],"equations":[45],"implemented":[46],"in":[47,61,74,162],"interior-point":[50,85],"solver":[51],"PIPS-IPM++.":[52],"The":[53,118],"algorithm":[54],"exploits":[55],"matrix":[57],"structure":[58,71],"commonly":[59],"found":[60],"optimization":[62,100],"problems:":[63],"doubly-bordered":[65],"block-diagonal":[66],"or":[67],"arrowhead":[68],"structure.":[69],"is":[72,103,133],"preserved":[73],"KKT":[77],"solved":[79],"during":[80],"each":[81],"iteration":[82],"method.":[86],"We":[87,140],"present":[88],"hierarchical":[90],"Schur":[91],"complement":[92],"that":[94],"distributes":[95],"solves":[97],"problem;":[101],"it":[102],"designed":[104],"high-performance":[106],"architectures":[107],"scales":[109],"well":[110],"with":[111],"availability":[113],"additional":[115],"computing":[116],"resources.":[117],"approach":[120,132],"uses":[121],"border":[123],"constraints'":[124],"locality":[125],"to":[126],"decouple":[127],"factorization":[129],"process.":[130],"Our":[131],"motivated":[134],"unit":[137],"commitment":[138],"problems.":[139],"demonstrate":[141],"performance":[143],"our":[145],"method":[146],"on":[147],"set":[149],"mid-to":[151],"instances,":[153],"some":[154],"which":[156],"have":[157],"more":[158],"than":[159],"10^9":[160],"nonzeros":[161],"their":[163],"constraint":[164],"matrix.":[165]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}