{"id":"https://openalex.org/W2009233589","doi":"https://doi.org/10.1007/s10107-009-0288-3","title":"Implications of the constant rank constraint qualification","display_name":"Implications of the constant rank constraint qualification","publication_year":2009,"publication_date":"2009-05-25","ids":{"openalex":"https://openalex.org/W2009233589","doi":"https://doi.org/10.1007/s10107-009-0288-3","mag":"2009233589"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-009-0288-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0288-3","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/A5101516861","display_name":"Shu L\u00fc","orcid":"https://orcid.org/0000-0002-4221-3093"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shu Lu","raw_affiliation_strings":["Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, 355 Hanes Hall, Chapel Hill, NC, 27599, USA","The University of North Carolina at Chapel Hill, Department of Statistics and Operations Research, 355 Hanes Hall, 27599, Chapel Hill, NC, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, 355 Hanes Hall, Chapel Hill, NC, 27599, USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"The University of North Carolina at Chapel Hill, Department of Statistics and Operations Research, 355 Hanes Hall, 27599, Chapel Hill, NC, USA#TAB#","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101516861"],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.881,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90453826,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"126","issue":"2","first_page":"365","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9944999814033508,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.993399977684021,"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":0.9812999963760376,"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/mathematics","display_name":"Mathematics","score":0.8598571419715881},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7079107761383057},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7074984312057495},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6779705882072449},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5976574420928955},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5596200227737427},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.555342435836792},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4902046322822571},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.4828353524208069},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4496843218803406},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4130645990371704},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.366626501083374},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3250504732131958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29343119263648987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13680410385131836},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07702317833900452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8598571419715881},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7079107761383057},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7074984312057495},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6779705882072449},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5976574420928955},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5596200227737427},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.555342435836792},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4902046322822571},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.4828353524208069},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4496843218803406},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4130645990371704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.366626501083374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3250504732131958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29343119263648987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13680410385131836},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07702317833900452},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-009-0288-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0288-3","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W36023795","https://openalex.org/W41323005","https://openalex.org/W65457436","https://openalex.org/W121392136","https://openalex.org/W217831350","https://openalex.org/W624148131","https://openalex.org/W637898570","https://openalex.org/W1511503348","https://openalex.org/W1522222833","https://openalex.org/W1537335979","https://openalex.org/W1543439990","https://openalex.org/W1567995217","https://openalex.org/W1607072065","https://openalex.org/W1970946112","https://openalex.org/W1975756369","https://openalex.org/W1982916564","https://openalex.org/W1991359458","https://openalex.org/W1992673508","https://openalex.org/W1993647205","https://openalex.org/W1996975947","https://openalex.org/W2003292231","https://openalex.org/W2014746566","https://openalex.org/W2018508199","https://openalex.org/W2018812345","https://openalex.org/W2022745738","https://openalex.org/W2031078227","https://openalex.org/W2036613704","https://openalex.org/W2042532613","https://openalex.org/W2060564235","https://openalex.org/W2072955130","https://openalex.org/W2079340989","https://openalex.org/W2081698249","https://openalex.org/W2083231020","https://openalex.org/W2097181689","https://openalex.org/W2097287227","https://openalex.org/W2111948593","https://openalex.org/W2158043848","https://openalex.org/W2326806701","https://openalex.org/W4212766343","https://openalex.org/W4231147659","https://openalex.org/W4231183558","https://openalex.org/W4246616525","https://openalex.org/W4249667877","https://openalex.org/W4252340393"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2385263368","https://openalex.org/W2347422947","https://openalex.org/W2061292372","https://openalex.org/W2112835755","https://openalex.org/W2353392568","https://openalex.org/W2807251790","https://openalex.org/W2377341410","https://openalex.org/W1454600515","https://openalex.org/W3157737852"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
