{"id":"https://openalex.org/W4309622438","doi":"https://doi.org/10.1137/21m1416552","title":"Efficient Preconditioners for Interior Point Methods via a New Schur Complement-Based Strategy","display_name":"Efficient Preconditioners for Interior Point Methods via a New Schur Complement-Based Strategy","publication_year":2022,"publication_date":"2022-11-22","ids":{"openalex":"https://openalex.org/W4309622438","doi":"https://doi.org/10.1137/21m1416552"},"language":"en","primary_location":{"id":"doi:10.1137/21m1416552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1416552","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5085780390","display_name":"Samah Karim","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samah Karim","raw_affiliation_strings":["Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (, )"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (, )","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022838370","display_name":"Edgar Solomonik","orcid":"https://orcid.org/0000-0002-6480-9066"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edgar Solomonik","raw_affiliation_strings":["Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (, )"],"raw_orcid":"https://orcid.org/0000-0002-6480-9066","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (, )","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085780390"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.3017,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60982438,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"43","issue":"4","first_page":"1680","last_page":"1711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.81453937292099},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8009786009788513},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.7990715503692627},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.7981840372085571},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.7205653190612793},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.693861186504364},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4842197895050049},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4283933639526367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41225746273994446},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3283466696739197},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.26128271222114563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.81453937292099},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8009786009788513},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.7990715503692627},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.7981840372085571},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.7205653190612793},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.693861186504364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4842197895050049},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4283933639526367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41225746273994446},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3283466696739197},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26128271222114563},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1416552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1416552","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":85,"referenced_works":["https://openalex.org/W203308545","https://openalex.org/W640673894","https://openalex.org/W1502854356","https://openalex.org/W1506342804","https://openalex.org/W1518039036","https://openalex.org/W1963751327","https://openalex.org/W1974348316","https://openalex.org/W1979359234","https://openalex.org/W1981315194","https://openalex.org/W1993397784","https://openalex.org/W1996982555","https://openalex.org/W2003550247","https://openalex.org/W2006751447","https://openalex.org/W2006884874","https://openalex.org/W2009629085","https://openalex.org/W2009926490","https://openalex.org/W2015605368","https://openalex.org/W2018279602","https://openalex.org/W2018850201","https://openalex.org/W2019779194","https://openalex.org/W2027634563","https://openalex.org/W2031691614","https://openalex.org/W2036870730","https://openalex.org/W2037144335","https://openalex.org/W2040474036","https://openalex.org/W2041563548","https://openalex.org/W2042281443","https://openalex.org/W2047515818","https://openalex.org/W2048360198","https://openalex.org/W2049219350","https://openalex.org/W2052602889","https://openalex.org/W2052996581","https://openalex.org/W2053050827","https://openalex.org/W2054034220","https://openalex.org/W2056828987","https://openalex.org/W2057565823","https://openalex.org/W2059511725","https://openalex.org/W2061519473","https://openalex.org/W2069671092","https://openalex.org/W2070419067","https://openalex.org/W2079361963","https://openalex.org/W2080090223","https://openalex.org/W2080514141","https://openalex.org/W2082001547","https://openalex.org/W2084461590","https://openalex.org/W2085378537","https://openalex.org/W2085581918","https://openalex.org/W2096801802","https://openalex.org/W2099359799","https://openalex.org/W2115329284","https://openalex.org/W2118431207","https://openalex.org/W2123871098","https://openalex.org/W2125422362","https://openalex.org/W2132894961","https://openalex.org/W2135988981","https://openalex.org/W2140153041","https://openalex.org/W2140803189","https://openalex.org/W2141870784","https://openalex.org/W2155216327","https://openalex.org/W2157590940","https://openalex.org/W2162057287","https://openalex.org/W2165375569","https://openalex.org/W2167322096","https://openalex.org/W2259982252","https://openalex.org/W2316564661","https://openalex.org/W2463887153","https://openalex.org/W2604122689","https://openalex.org/W2606969936","https://openalex.org/W2753635573","https://openalex.org/W2804722640","https://openalex.org/W2895332762","https://openalex.org/W2914327614","https://openalex.org/W2922189284","https://openalex.org/W2940731840","https://openalex.org/W2964263181","https://openalex.org/W2995987820","https://openalex.org/W3047012757","https://openalex.org/W3100929843","https://openalex.org/W3102568135","https://openalex.org/W3104106909","https://openalex.org/W3154088878","https://openalex.org/W4212997115","https://openalex.org/W4232109906","https://openalex.org/W4301283118","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W2500884246","https://openalex.org/W4297074229","https://openalex.org/W2963441829","https://openalex.org/W2159515580","https://openalex.org/W2081820376","https://openalex.org/W2082290366","https://openalex.org/W2277328098","https://openalex.org/W1964968800","https://openalex.org/W2091325992","https://openalex.org/W2059625160"],"abstract_inverted_index":{".We":[0],"propose":[1,101],"a":[2,27,194,199],"novel":[3],"preconditioned":[4,22,165,191,209],"inexact":[5,166],"primal-dual":[6,92],"interior":[7,69,93,167,215],"point":[8,70,94,168,216],"method":[9,25,119,186,210],"for":[10,78,110,182,211],"constrained":[11],"convex":[12],"quadratic":[13,159],"programming":[14,160],"problems.":[15],"The":[16],"algorithm":[17],"we":[18,47,100],"describe":[19],"invokes":[20],"the":[21,43,52,55,79,85,98,105,111,116,127,135,140,157,184,206],"conjugate":[23,117],"gradient":[24,118],"on":[26],"new":[28,74],"reduced":[29,81],"Schur":[30,44],"complement":[31,45],"Karush\u2013Kuhn\u2013Tucker":[32],"(KKT)":[33],"system":[34,82],"in":[35,91,196],"implicit":[36],"form.":[37],"In":[38],"contrast":[39],"to":[40,63,205],"standard":[41],"approaches,":[42],"formulation":[46],"consider":[48],"enables":[49],"reuse":[50],"of":[51,54,97,107,129,142,145,202],"factorization":[53],"KKT":[56],"matrix":[57,113],"with":[58,88,151],"rows":[59],"and":[60,114,154,175],"columns":[61],"corresponding":[62],"inequality":[64],"constraints":[65,131],"excluded":[66],"across":[67],"all":[68,179],"iterations.":[71],"Further,":[72],"two":[73],"preconditioners":[75,99],"are":[76,170],"presented":[77],"resulting":[80],"that":[83,163],"alleviate":[84],"ill-conditioning":[86],"associated":[87],"slack":[89],"variables":[90],"methods.":[95],"Each":[96],"also":[102],"provably":[103],"reduces":[104],"number":[106,128,141],"unique":[108],"eigenvalues":[109],"coefficient":[112],"thus":[115],"iteration":[120],"count.":[121],"One":[122],"preconditioner":[123],"is":[124,132,137,147,187],"efficient":[125,138],"when":[126,139],"equality":[130],"small,":[133],"while":[134],"other":[136],"remaining":[143],"degrees":[144],"freedom":[146],"small.":[148],"Numerical":[149],"experiments":[150],"synthetic":[152],"problems":[153,155,181],"from":[156],"Maros\u2013M\u00e9sz\u00e1ros":[158],"collection":[161],"show":[162],"our":[164,190],"solvers":[169],"effective":[171],"at":[172],"improving":[173],"conditioning":[174],"reducing":[176],"cost.":[177],"Across":[178],"test":[180],"which":[183],"direct":[185],"not":[188],"fastest,":[189],"methods":[192],"achieve":[193],"reduction":[195],"cost":[197],"by":[198],"geometric":[200],"mean":[201],"1.432":[203],"relative":[204],"best":[207],"alternative":[208],"each":[212],"problem.KeywordsKKT":[213],"systemsprimal-dual":[214],"methodsKrylov":[217],"subspace":[218],"methodspreconditioningMSC":[219],"codes65F0865F1065F5065K05":[220]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
