{"id":"https://openalex.org/W2234116669","doi":"https://doi.org/10.1007/s11590-007-0074-1","title":"Exact L 2-norm plane separation","display_name":"Exact L 2-norm plane separation","publication_year":2008,"publication_date":"2008-02-14","ids":{"openalex":"https://openalex.org/W2234116669","doi":"https://doi.org/10.1007/s11590-007-0074-1","mag":"2234116669"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-007-0074-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-007-0074-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","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/A5089929904","display_name":"Charles Audet","orcid":"https://orcid.org/0000-0002-3043-5393"},"institutions":[{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]},{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Charles Audet","raw_affiliation_strings":["GERAD and \u00c9cole Polytechnique de Montr\u00e9al, C.P. 6079, station Centre-ville, Montreal, QC, Canada, H3C 3A7"],"affiliations":[{"raw_affiliation_string":"GERAD and \u00c9cole Polytechnique de Montr\u00e9al, C.P. 6079, station Centre-ville, Montreal, QC, Canada, H3C 3A7","institution_ids":["https://openalex.org/I45683168","https://openalex.org/I4210133247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038480864","display_name":"Pierre Hansen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pierre Hansen","raw_affiliation_strings":["GERAD and HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7"],"affiliations":[{"raw_affiliation_string":"GERAD and HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7","institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077222585","display_name":"Alejandro Karam","orcid":null},"institutions":[{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alejandro Karam","raw_affiliation_strings":["HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7"],"affiliations":[{"raw_affiliation_string":"HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7","institution_ids":["https://openalex.org/I108192572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055363976","display_name":"C.T. Ng","orcid":"https://orcid.org/0000-0003-0020-8234"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Chi To Ng","raw_affiliation_strings":["Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105531584","display_name":"Sylvain Perron","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Sylvain Perron","raw_affiliation_strings":["GERAD and HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7"],"affiliations":[{"raw_affiliation_string":"GERAD and HEC Montr\u00e9al, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montreal, QC, Canada, H3T 2A7","institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5105531584"],"corresponding_institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.062,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8704334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"483","last_page":"495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976999759674072,"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":0.9976999759674072,"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":0.9975000023841858,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6675124168395996},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6616092920303345},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5791379809379578},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.5517786741256714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5517513155937195},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5489988923072815},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5391775369644165},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.43548017740249634},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4182705879211426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38891923427581787},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.362568199634552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3560580313205719},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.306635320186615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17829236388206482},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13872668147087097}],"concepts":[{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6675124168395996},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6616092920303345},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5791379809379578},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.5517786741256714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5517513155937195},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5489988923072815},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5391775369644165},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.43548017740249634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4182705879211426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38891923427581787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.362568199634552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3560580313205719},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.306635320186615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17829236388206482},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13872668147087097},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11590-007-0074-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-007-0074-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/29676","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/29676","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"},{"id":"pmh:oai:publications.polymtl.ca:21170","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/21170/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.46000000834465027,"display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1530501119","https://openalex.org/W1543095928","https://openalex.org/W1546839024","https://openalex.org/W1561593890","https://openalex.org/W1974208065","https://openalex.org/W1985469991","https://openalex.org/W1992919040","https://openalex.org/W1995665109","https://openalex.org/W1996470358","https://openalex.org/W2003457692","https://openalex.org/W2010334716","https://openalex.org/W2014076886","https://openalex.org/W2048881327","https://openalex.org/W2051381803","https://openalex.org/W2063190731","https://openalex.org/W2069231281","https://openalex.org/W2073429525","https://openalex.org/W2081929325","https://openalex.org/W2084812512","https://openalex.org/W2117907815","https://openalex.org/W2156382728","https://openalex.org/W2170720453","https://openalex.org/W3112020351","https://openalex.org/W6643631338"],"related_works":["https://openalex.org/W2370815826","https://openalex.org/W2433057514","https://openalex.org/W2373436826","https://openalex.org/W2167961874","https://openalex.org/W4292026839","https://openalex.org/W2363214567","https://openalex.org/W2978550247","https://openalex.org/W1854082044","https://openalex.org/W3169007055","https://openalex.org/W4237047059"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}