{"id":"https://openalex.org/W2008195537","doi":"https://doi.org/10.1137/s1052623495287927","title":"Abadie's Constraint Qualification, Metric Regularity, and Error Bounds for Differentiable Convex Inequalities","display_name":"Abadie's Constraint Qualification, Metric Regularity, and Error Bounds for Differentiable Convex Inequalities","publication_year":1997,"publication_date":"1997-11-01","ids":{"openalex":"https://openalex.org/W2008195537","doi":"https://doi.org/10.1137/s1052623495287927","mag":"2008195537"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623495287927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623495287927","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5100326378","display_name":"Wu Li","orcid":"https://orcid.org/0000-0001-7115-1517"},"institutions":[{"id":"https://openalex.org/I81365321","display_name":"Old Dominion University","ror":"https://ror.org/04zjtrb98","country_code":"US","type":"education","lineage":["https://openalex.org/I81365321"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wu Li","raw_affiliation_strings":["Old Dominion University,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Old Dominion University,","institution_ids":["https://openalex.org/I81365321"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100326378"],"corresponding_institution_ids":["https://openalex.org/I81365321"],"apc_list":null,"apc_paid":null,"fwci":7.671,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.97678275,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"966","last_page":"978"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8794560432434082},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7851826548576355},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6513628363609314},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5978748202323914},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5551950335502625},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5373709797859192},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5373676419258118},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5322316288948059},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5187097191810608},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.48823073506355286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45025670528411865},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.44756168127059937},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4424903988838196},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.40555864572525024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3654637336730957},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3580104112625122},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3217667043209076},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07686024904251099}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8794560432434082},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7851826548576355},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6513628363609314},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5978748202323914},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5551950335502625},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5373709797859192},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5373676419258118},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5322316288948059},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5187097191810608},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.48823073506355286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45025670528411865},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.44756168127059937},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4424903988838196},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.40555864572525024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3654637336730957},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3580104112625122},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3217667043209076},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07686024904251099},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1052623495287927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623495287927","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6399999856948853,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1553702074","https://openalex.org/W1964879221","https://openalex.org/W1975017829","https://openalex.org/W1976772621","https://openalex.org/W1978320424","https://openalex.org/W1982325686","https://openalex.org/W1983871704","https://openalex.org/W1990883342","https://openalex.org/W1991607307","https://openalex.org/W1992769584","https://openalex.org/W2002854334","https://openalex.org/W2011925679","https://openalex.org/W2013850411","https://openalex.org/W2018508199","https://openalex.org/W2024483461","https://openalex.org/W2024828886","https://openalex.org/W2029084473","https://openalex.org/W2033604629","https://openalex.org/W2047341913","https://openalex.org/W2054803831","https://openalex.org/W2061907550","https://openalex.org/W2064449121","https://openalex.org/W2072058266","https://openalex.org/W2074857865","https://openalex.org/W2085154531","https://openalex.org/W2090084467","https://openalex.org/W2093417350","https://openalex.org/W2095929557","https://openalex.org/W2152113502","https://openalex.org/W2153745131","https://openalex.org/W2334285086","https://openalex.org/W3000651840","https://openalex.org/W4248231329","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W3105173213","https://openalex.org/W942533424","https://openalex.org/W2049339417","https://openalex.org/W2097846334","https://openalex.org/W108799873","https://openalex.org/W2531699496","https://openalex.org/W4301135054","https://openalex.org/W1968850685","https://openalex.org/W2072707988","https://openalex.org/W2356958610"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,27,48],"study":[4],"differentiable":[5],"convex":[6,24,59],"inequalities":[7],"and":[8,13,39],"prove":[9],"that":[10,29],"metric":[11,30],"regularity":[12],"Abadie's":[14,40],"constraint":[15],"qualification":[16],"(CQ)":[17],"are":[18,42],"equivalent":[19],"for":[20],"such":[21],"inequalities.":[22],"For":[23],"quadratic":[25,60],"inequalities,":[26],"show":[28],"regularity,":[31],"the":[32],"existence":[33],"of":[34,53,57],"a":[35,46,58],"global":[36],"error":[37],"bound,":[38],"CQ":[41],"mutually":[43],"equivalent.":[44],"As":[45],"consequence,":[47],"derive":[49],"two":[50],"new":[51],"characterizations":[52],"weak":[54],"sharp":[55],"minima":[56],"programming":[61],"problem.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
