{"id":"https://openalex.org/W4390098307","doi":"https://doi.org/10.1109/focs57990.2023.00123","title":"Interior-point methods on manifolds: theory and applications","display_name":"Interior-point methods on manifolds: theory and applications","publication_year":2023,"publication_date":"2023-11-06","ids":{"openalex":"https://openalex.org/W4390098307","doi":"https://doi.org/10.1109/focs57990.2023.00123"},"language":"en","primary_location":{"id":"doi:10.1109/focs57990.2023.00123","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs57990.2023.00123","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-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/A5090989020","display_name":"Hiroshi Hirai","orcid":"https://orcid.org/0000-0002-4784-5110"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroshi Hirai","raw_affiliation_strings":["Nagoya University,Graduate School of Mathematics,Nagoya,Japan","Graduate School of Mathematics, Nagoya University, Nagoya, Japan"],"affiliations":[{"raw_affiliation_string":"Nagoya University,Graduate School of Mathematics,Nagoya,Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"Graduate School of Mathematics, Nagoya University, Nagoya, Japan","institution_ids":["https://openalex.org/I60134161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011111072","display_name":"Harold Nieuwboer","orcid":"https://orcid.org/0000-0003-3627-3636"},"institutions":[{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Harold Nieuwboer","raw_affiliation_strings":["University of Amsterdam,Korteweg-de Vries Institute and QuSoft,Amsterdam,The Netherlands","Korteweg-de Vries Institute and QuSoft, University of Amsterdam, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"University of Amsterdam,Korteweg-de Vries Institute and QuSoft,Amsterdam,The Netherlands","institution_ids":["https://openalex.org/I4210099082"]},{"raw_affiliation_string":"Korteweg-de Vries Institute and QuSoft, University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I4210099082","https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008194188","display_name":"Michael Walter","orcid":"https://orcid.org/0000-0001-6679-2491"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Walter","raw_affiliation_strings":["Ruhr University Bochum,Faculty of Computer Science,Bochum,Germany","Faculty of Computer Science, Ruhr University Bochum, Bochum, Germany"],"affiliations":[{"raw_affiliation_string":"Ruhr University Bochum,Faculty of Computer Science,Bochum,Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"Faculty of Computer Science, Ruhr University Bochum, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090989020"],"corresponding_institution_ids":["https://openalex.org/I60134161"],"apc_list":null,"apc_paid":null,"fwci":3.3172,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.92873275,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2021","last_page":"2030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"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":0.9975000023841858,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.996399998664856,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9769999980926514,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.573788046836853},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5459874272346497},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.5262849926948547},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5217079520225525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5195096731185913},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4955514669418335},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4802730083465576},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4603033661842346},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41644665598869324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4012244641780853},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3905841112136841},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3680172264575958},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2490491271018982},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.142091304063797},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12576499581336975}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.573788046836853},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5459874272346497},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.5262849926948547},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5217079520225525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5195096731185913},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4955514669418335},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4802730083465576},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4603033661842346},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41644665598869324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4012244641780853},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3905841112136841},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3680172264575958},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2490491271018982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.142091304063797},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12576499581336975},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/focs57990.2023.00123","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs57990.2023.00123","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":87,"referenced_works":["https://openalex.org/W103900042","https://openalex.org/W1572341022","https://openalex.org/W1601957988","https://openalex.org/W1632601927","https://openalex.org/W1894723027","https://openalex.org/W1966991151","https://openalex.org/W1970928279","https://openalex.org/W1979502700","https://openalex.org/W1982828906","https://openalex.org/W1983894121","https://openalex.org/W1987953347","https://openalex.org/W2005470559","https://openalex.org/W2015604011","https://openalex.org/W2022204379","https://openalex.org/W2029494882","https://openalex.org/W2032929786","https://openalex.org/W2033040247","https://openalex.org/W2053997972","https://openalex.org/W2066214692","https://openalex.org/W2074763854","https://openalex.org/W2076680677","https://openalex.org/W2080809355","https://openalex.org/W2087728971","https://openalex.org/W2092736015","https://openalex.org/W2125391899","https://openalex.org/W2132463883","https://openalex.org/W2134086356","https://openalex.org/W2152422059","https://openalex.org/W2154059477","https://openalex.org/W2157491291","https://openalex.org/W2158131535","https://openalex.org/W2164118370","https://openalex.org/W2254435734","https://openalex.org/W2294294273","https://openalex.org/W2410099853","https://openalex.org/W2610466503","https://openalex.org/W2610680804","https://openalex.org/W2611147814","https://openalex.org/W2769660485","https://openalex.org/W2797346236","https://openalex.org/W2896405912","https://openalex.org/W2901108323","https://openalex.org/W2962719003","https://openalex.org/W2962763948","https://openalex.org/W2962968674","https://openalex.org/W2963595145","https://openalex.org/W2963637877","https://openalex.org/W2964051254","https://openalex.org/W2964063683","https://openalex.org/W2968709464","https://openalex.org/W2971476396","https://openalex.org/W2980475696","https://openalex.org/W3002603762","https://openalex.org/W3013951206","https://openalex.org/W3014036233","https://openalex.org/W3076268892","https://openalex.org/W3099629744","https://openalex.org/W3103171021","https://openalex.org/W3106328136","https://openalex.org/W3111638709","https://openalex.org/W3128045178","https://openalex.org/W3130811428","https://openalex.org/W3215919055","https://openalex.org/W3216339223","https://openalex.org/W4205293427","https://openalex.org/W4210293807","https://openalex.org/W4221163624","https://openalex.org/W4246883249","https://openalex.org/W4286904181","https://openalex.org/W4287389869","https://openalex.org/W4297786942","https://openalex.org/W4301216918","https://openalex.org/W4303111105","https://openalex.org/W4311431696","https://openalex.org/W4313890592","https://openalex.org/W4323539420","https://openalex.org/W4387160166","https://openalex.org/W4387701368","https://openalex.org/W4390098167","https://openalex.org/W4390098307","https://openalex.org/W6682962330","https://openalex.org/W6684688338","https://openalex.org/W6694978291","https://openalex.org/W6756055649","https://openalex.org/W6758062163","https://openalex.org/W6773347617","https://openalex.org/W6791459244"],"related_works":["https://openalex.org/W2094662834","https://openalex.org/W3037672488","https://openalex.org/W2008939113","https://openalex.org/W2029691756","https://openalex.org/W1992520655","https://openalex.org/W4295884766","https://openalex.org/W2105228010","https://openalex.org/W164473625","https://openalex.org/W4281992692","https://openalex.org/W4302084106"],"abstract_inverted_index":{"Interior-point":[0],"methods":[1],"offer":[2],"a":[3,26,31,65,73,80,117],"highly":[4],"versatile":[5],"framework":[6],"for":[7,68,76,135,158,163],"convex":[8,74],"optimization":[9,143],"that":[10,24,41,102],"is":[11,23,119],"effective":[12],"in":[13,20,51,55,90,171],"theory":[14,22],"and":[15,39,48,83,100,109,141,152,168],"practice.":[16],"A":[17],"key":[18],"notion":[19],"their":[21],"of":[25,34,60,98,106,125,139,148],"self-concordant":[27,81],"barrier.":[28],"We":[29,63,94],"give":[30,129],"suitable":[32],"generalization":[33],"self-concordance":[35],"to":[36,116],"Riemannian":[37],"manifolds":[38],"show":[40,101],"it":[42],"gives":[43],"the":[44,52,85,91,104,113,123,136,155],"same":[45],"structural":[46],"results":[47],"guarantees":[49,88,134],"as":[50,89],"Euclidean":[53,92],"setting,":[54],"particular":[56],"local":[57],"quadratic":[58],"convergence":[59],"Newton\u2019s":[61],"method.":[62],"analyze":[64],"path-following":[66],"method":[67],"optimizing":[69],"compatible":[70],"objectives":[71],"over":[72],"domain":[75],"which":[77,145],"one":[78],"has":[79],"barrier,":[82],"obtain":[84],"standard":[86],"complexity":[87,133],"setting.":[93],"provide":[95,154],"general":[96,137],"constructions":[97],"barriers,":[99],"on":[103],"space":[105],"positive-definite":[107],"matrices":[108],"other":[110],"symmetric":[111],"spaces,":[112],"squared":[114],"distance":[115],"point":[118],"self-concordant.":[120],"To":[121],"demonstrate":[122],"versatility":[124],"our":[126],"framework,":[127],"we":[128,153],"algorithms":[130,157],"with":[131],"state-of-the-art":[132],"class":[138],"scaling":[140],"non-commutative":[142],"problems,":[144],"have":[146],"been":[147],"much":[149],"recent":[150],"interest,":[151],"first":[156],"efficiently":[159],"finding":[160],"high-precision":[161],"solutions":[162],"computing":[164],"minimal":[165],"enclosing":[166],"balls":[167],"geometric":[169],"medians":[170],"non-positive":[172],"curvature.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}