{"id":"https://openalex.org/W1984826350","doi":"https://doi.org/10.1137/130911287","title":"Quasi-Slater and Farkas--Minkowski Qualifications for Semi-infinite Programming with Applications","display_name":"Quasi-Slater and Farkas--Minkowski Qualifications for Semi-infinite Programming with Applications","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1984826350","doi":"https://doi.org/10.1137/130911287","mag":"1984826350"},"language":"en","primary_location":{"id":"doi:10.1137/130911287","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911287","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/A5100424917","display_name":"Chong Li","orcid":"https://orcid.org/0000-0001-7097-4220"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chong Li","raw_affiliation_strings":["Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056442662","display_name":"Xiaopeng Zhao","orcid":"https://orcid.org/0000-0003-1207-5379"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaopeng Zhao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101868817","display_name":"Yaohua Hu","orcid":"https://orcid.org/0000-0001-6412-5804"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaohua Hu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100424917"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":2.1752,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87048173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"4","first_page":"2208","last_page":"2230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9977999925613403,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8150761723518372},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6799235939979553},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5748609900474548},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.5516977906227112},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.5269304513931274},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.49995946884155273},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4887668788433075},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46023961901664734},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43492040038108826},{"id":"https://openalex.org/keywords/geometric-programming","display_name":"Geometric programming","score":0.4315067529678345},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4023898243904114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3352477550506592},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31042608618736267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11450514197349548},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07799991965293884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8150761723518372},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6799235939979553},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5748609900474548},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.5516977906227112},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.5269304513931274},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.49995946884155273},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4887668788433075},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46023961901664734},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43492040038108826},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.4315067529678345},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4023898243904114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3352477550506592},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31042608618736267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11450514197349548},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07799991965293884},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130911287","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911287","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W83112366","https://openalex.org/W1503425191","https://openalex.org/W1545324631","https://openalex.org/W1553702074","https://openalex.org/W1555801467","https://openalex.org/W1967505494","https://openalex.org/W1974680989","https://openalex.org/W1989721897","https://openalex.org/W1990600811","https://openalex.org/W1993798057","https://openalex.org/W1999619808","https://openalex.org/W2006581042","https://openalex.org/W2007257992","https://openalex.org/W2008096467","https://openalex.org/W2008602023","https://openalex.org/W2011840608","https://openalex.org/W2019651381","https://openalex.org/W2021295607","https://openalex.org/W2037005512","https://openalex.org/W2044845604","https://openalex.org/W2047483985","https://openalex.org/W2051384161","https://openalex.org/W2062662841","https://openalex.org/W2063449703","https://openalex.org/W2064099700","https://openalex.org/W2070409288","https://openalex.org/W2072822417","https://openalex.org/W2075979998","https://openalex.org/W2087446297","https://openalex.org/W2092191703","https://openalex.org/W2094211749","https://openalex.org/W2129894900","https://openalex.org/W2136553956","https://openalex.org/W2769907661"],"related_works":["https://openalex.org/W2286777929","https://openalex.org/W2950428426","https://openalex.org/W4293050169","https://openalex.org/W960999769","https://openalex.org/W2046207812","https://openalex.org/W4309277470","https://openalex.org/W2605451175","https://openalex.org/W2936973291","https://openalex.org/W1979971434","https://openalex.org/W4211088175"],"abstract_inverted_index":{"The":[0],"well-known":[1],"Farkas--Minkowski":[2],"(FM)":[3],"type":[4,54],"qualification":[5,59],"plays":[6],"an":[7],"important":[8],"role":[9],"in":[10,22],"linear":[11],"semi-infinite":[12,30,45],"programming":[13],"and":[14,27,49,80,86,97],"has":[15],"been":[16],"extensively":[17],"developed":[18],"by":[19],"many":[20],"authors":[21],"establishing":[23],"optimality":[24],"conditions,":[25],"duality,":[26],"stability":[28],"for":[29,43,82,91],"programming.":[31],"In":[32],"this":[33],"paper,":[34],"we":[35,74],"introduce":[36],"the":[37,40,52,57,66,93],"concept":[38],"of":[39,65],"quasi-Slater":[41],"condition":[42],"a":[44],"convex":[46],"inequality":[47],"system":[48],"present":[50],"that":[51],"Slater":[53],"conditions":[55,90],"imply":[56],"FM":[58],"under":[60],"some":[61,88],"appropriate":[62],"continuity":[63],"assumption":[64],"set-valued":[67],"mapping":[68],"$i\\mapsto":[69],"f_i(x)$.":[70],"Applying":[71],"these":[72],"relationships,":[73],"establish":[75],"dual":[76],"characterizations,":[77],"both":[78],"asymptotic":[79],"nonasymptotic,":[81],"set":[83],"containment":[84],"problems":[85],"provide":[87],"sufficient":[89],"ensuring":[92],"strong":[94],"Lagrangian":[95],"duality":[96],"Farkas":[98],"lemma.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}