{"id":"https://openalex.org/W4221144045","doi":"https://doi.org/10.1007/s10957-022-02076-1","title":"Computing Conjugate Barrier Information for Nonsymmetric Cones","display_name":"Computing Conjugate Barrier Information for Nonsymmetric Cones","publication_year":2022,"publication_date":"2022-08-20","ids":{"openalex":"https://openalex.org/W4221144045","doi":"https://doi.org/10.1007/s10957-022-02076-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-022-02076-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02076-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02076-1.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02076-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067967881","display_name":"Lea Kapelevich","orcid":"https://orcid.org/0000-0002-1043-393X"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lea Kapelevich","raw_affiliation_strings":["Operations Research Center, MIT, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1043-393X","affiliations":[{"raw_affiliation_string":"Operations Research Center, MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075207555","display_name":"Erling Andersen","orcid":"https://orcid.org/0000-0001-8268-1206"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erling D. Andersen","raw_affiliation_strings":["MOSEK ApS, Copenhagen, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOSEK ApS, Copenhagen, Denmark","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008961628","display_name":"Juan Pablo Vielma","orcid":"https://orcid.org/0000-0003-4335-7248"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan Pablo Vielma","raw_affiliation_strings":["Google Research and MIT Sloan School of Management, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Research and MIT Sloan School of Management, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067967881"],"corresponding_institution_ids":["https://openalex.org/I4210110987"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0289769,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"202","issue":"1","first_page":"271","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.19280000030994415,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.19280000030994415,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.18729999661445618,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.11429999768733978,"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/conjugate","display_name":"Conjugate","score":0.7944673299789429},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7082738876342773},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6480436325073242},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5307283997535706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5292640924453735},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.5010271072387695},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4874017834663391},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4562346935272217},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4477599859237671},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4400365948677063},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3739827871322632},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3449477553367615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22476890683174133},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11616981029510498}],"concepts":[{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.7944673299789429},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7082738876342773},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6480436325073242},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5307283997535706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5292640924453735},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.5010271072387695},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4874017834663391},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4562346935272217},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4477599859237671},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4400365948677063},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3739827871322632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3449477553367615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22476890683174133},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11616981029510498},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10957-022-02076-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02076-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02076-1.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2201.04121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.04121","pdf_url":"https://arxiv.org/pdf/2201.04121","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:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02076-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-022-02076-1","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"},{"id":"pmh:oai:dspace.mit.edu:1721.1/144398","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/144398","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Springer US","raw_type":"http://purl.org/eprint/type/JournalArticle"},{"id":"doi:10.48550/arxiv.2201.04121","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2201.04121","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10957-022-02076-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02076-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02076-1.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3139513672","display_name":null,"funder_award_id":"OAC-1835443","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7641931476","display_name":"Framework: Software: Next-Generation Cyberinfrastructure for Large-Scale Computer-Based Scientific Analysis and Discovery","funder_award_id":"1835443","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8419555931","display_name":null,"funder_award_id":"N00014-18-1-2079","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221144045.pdf","grobid_xml":"https://content.openalex.org/works/W4221144045.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W145128891","https://openalex.org/W280536263","https://openalex.org/W1632601927","https://openalex.org/W1806104592","https://openalex.org/W1999613943","https://openalex.org/W2021428356","https://openalex.org/W2030828780","https://openalex.org/W2058404049","https://openalex.org/W2085850581","https://openalex.org/W2090084096","https://openalex.org/W2093249882","https://openalex.org/W2114408464","https://openalex.org/W2117065890","https://openalex.org/W2143904249","https://openalex.org/W2786116690","https://openalex.org/W2901838001","https://openalex.org/W3133541217","https://openalex.org/W3181648109","https://openalex.org/W3182400646","https://openalex.org/W3197081982","https://openalex.org/W3210990630"],"related_works":["https://openalex.org/W468616","https://openalex.org/W9913564","https://openalex.org/W7609366","https://openalex.org/W11631616","https://openalex.org/W5309060","https://openalex.org/W4878001","https://openalex.org/W10353523","https://openalex.org/W1662918","https://openalex.org/W12539047","https://openalex.org/W10332844"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"recent":[2],"interior":[3],"point":[4],"algorithm":[5],"by":[6],"Dahl":[7],"and":[8],"Andersen":[9],"[10]":[10],"for":[11,66,77,81,86],"nonsymmetric":[12,69],"cones":[13,33],"as":[14,16],"well":[15],"earlier":[17],"works":[18],"[18,":[19],"21]":[20],"require":[21],"derivative":[22],"information":[23,49],"from":[24],"the":[25,28,32,35,59,62,82,87],"conjugate":[26,63],"of":[27,31,46,61],"barrier":[29,64],"function":[30,65],"in":[34],"problem.":[36],"Besides":[37],"a":[38],"few":[39],"special":[40],"cases,":[41,73],"there":[42],"is":[43,50,75],"no":[44],"indication":[45],"when":[47],"this":[48,74],"efficient":[51],"to":[52,57],"evaluate.":[53],"We":[54],"show":[55],"how":[56],"compute":[58],"gradient":[60],"seven":[67],"useful":[68],"cones.":[70],"In":[71],"some":[72],"helpful":[76],"deriving":[78],"closed-form":[79],"expressions":[80],"inverse":[83],"Hessian":[84],"operator":[85],"primal":[88],"barrier.":[89]},"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}