{"id":"https://openalex.org/W2154059477","doi":"https://doi.org/10.1007/s102080010032","title":"On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods","display_name":"On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods","publication_year":2002,"publication_date":"2002-10-17","ids":{"openalex":"https://openalex.org/W2154059477","doi":"https://doi.org/10.1007/s102080010032","mag":"2154059477"},"language":"en","primary_location":{"id":"doi:10.1007/s102080010032","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s102080010032","pdf_url":null,"source":{"id":"https://openalex.org/S192217950","display_name":"Mathematische Annalen","issn_l":"0025-5831","issn":["0025-5831","1432-1807"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","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/A5108665803","display_name":"Yu. E. Nesterov","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Yu. E. Nesterov","raw_affiliation_strings":["CORE, Catholic University of Louvain, Louvain-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CORE, Catholic University of Louvain, Louvain-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017907148","display_name":"Mike Todd","orcid":"https://orcid.org/0000-0002-0042-0713"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. J. Todd","raw_affiliation_strings":["School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.6474,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.9499888,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2","issue":"4","first_page":"333","last_page":"361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9948999881744385,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9948999881744385,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9919000267982483,"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/T10136","display_name":"Statistical Methods and Inference","score":0.95169997215271,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.8367680311203003},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.720842719078064},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6507991552352905},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6236718893051147},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5086380243301392},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5033957362174988},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.4957636296749115},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4760984182357788},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.46484464406967163},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.46232298016548157},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.453920841217041},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4434695541858673},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43970316648483276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3900015652179718},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.21574679017066956},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21026703715324402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8367680311203003},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.720842719078064},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6507991552352905},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6236718893051147},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5086380243301392},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5033957362174988},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.4957636296749115},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4760984182357788},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.46484464406967163},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.46232298016548157},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.453920841217041},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4434695541858673},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43970316648483276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3900015652179718},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.21574679017066956},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21026703715324402},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s102080010032","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s102080010032","pdf_url":null,"source":{"id":"https://openalex.org/S192217950","display_name":"Mathematische Annalen","issn_l":"0025-5831","issn":["0025-5831","1432-1807"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:cor:louvrp:1595","is_oa":false,"landing_page_url":"http://doi.org/10.1007/s102080010032","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":"","raw_type":"preprint"},{"id":"pmh:oai:dial.uclouvain.be:boreal:23384","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/23384","pdf_url":null,"source":{"id":"https://openalex.org/S4306400166","display_name":"Digital Access to Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800384882","host_organization_name":"Harris County Public Library","host_organization_lineage":["https://openalex.org/I2800384882"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of Computational Mathematics, Vol. 2, no. 4, p. 333-361 (2002)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1518039036","https://openalex.org/W1814618093","https://openalex.org/W1984617485","https://openalex.org/W1999031104","https://openalex.org/W2020706127","https://openalex.org/W2045512849","https://openalex.org/W2087640086","https://openalex.org/W2093249882","https://openalex.org/W2114408464","https://openalex.org/W2157590940","https://openalex.org/W2611147814"],"related_works":["https://openalex.org/W4353103777","https://openalex.org/W2950657073","https://openalex.org/W2951269968","https://openalex.org/W2161938318","https://openalex.org/W2946352054","https://openalex.org/W3127827089","https://openalex.org/W1486814401","https://openalex.org/W4293874102","https://openalex.org/W2130044423","https://openalex.org/W2991226590"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}