{"id":"https://openalex.org/W2001451578","doi":"https://doi.org/10.1007/s10107-011-0496-5","title":"Convex envelopes generated from finitely many compact convex sets","display_name":"Convex envelopes generated from finitely many compact convex sets","publication_year":2011,"publication_date":"2011-10-27","ids":{"openalex":"https://openalex.org/W2001451578","doi":"https://doi.org/10.1007/s10107-011-0496-5","mag":"2001451578"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-011-0496-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-011-0496-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5059503583","display_name":"Aida Khajavirad","orcid":"https://orcid.org/0000-0002-7097-1676"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Aida Khajavirad","raw_affiliation_strings":["Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031811254","display_name":"Nikolaos V. Sahinidis","orcid":"https://orcid.org/0000-0003-2087-9131"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikolaos V. Sahinidis","raw_affiliation_strings":["Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059503583"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.5044,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.95416398,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"137","issue":"1-2","first_page":"371","last_page":"408"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.987500011920929,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9837999939918518,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8056159615516663},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.7067663073539734},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.7031900882720947},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.6738213896751404},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.6667208075523376},{"id":"https://openalex.org/keywords/absolutely-convex-set","display_name":"Absolutely convex set","score":0.5648611187934875},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5455490946769714},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5087459683418274},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.48105621337890625},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4745265543460846},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4403066337108612},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42942118644714355},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.41670486330986023},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33850130438804626},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09002113342285156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8056159615516663},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.7067663073539734},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.7031900882720947},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.6738213896751404},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.6667208075523376},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.5648611187934875},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5455490946769714},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5087459683418274},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48105621337890625},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4745265543460846},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4403066337108612},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42942118644714355},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.41670486330986023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33850130438804626},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09002113342285156},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-011-0496-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-011-0496-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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":34,"referenced_works":["https://openalex.org/W389907844","https://openalex.org/W633277346","https://openalex.org/W1497465005","https://openalex.org/W1498671329","https://openalex.org/W1503425191","https://openalex.org/W1526206232","https://openalex.org/W1542918674","https://openalex.org/W1968143987","https://openalex.org/W1972997295","https://openalex.org/W1983127118","https://openalex.org/W1988622494","https://openalex.org/W1998221953","https://openalex.org/W2004407575","https://openalex.org/W2005320876","https://openalex.org/W2021674665","https://openalex.org/W2023672624","https://openalex.org/W2026063499","https://openalex.org/W2048881327","https://openalex.org/W2049505431","https://openalex.org/W2056337104","https://openalex.org/W2068054962","https://openalex.org/W2077654805","https://openalex.org/W2078327411","https://openalex.org/W2080116182","https://openalex.org/W2084006722","https://openalex.org/W2093022060","https://openalex.org/W2129790367","https://openalex.org/W2155258508","https://openalex.org/W2157195803","https://openalex.org/W2170569252","https://openalex.org/W2482182218","https://openalex.org/W2505968561","https://openalex.org/W4253741566","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2026600343","https://openalex.org/W2391247224","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W3092518081","https://openalex.org/W2002037426","https://openalex.org/W1978014154","https://openalex.org/W4361807553","https://openalex.org/W2040676043","https://openalex.org/W2356261519"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}