{"id":"https://openalex.org/W3092190404","doi":"https://doi.org/10.1137/19m1281678","title":"Convex Analysis in $\\mathbb{Z}^n$ and Applications to Integer Linear Programming","display_name":"Convex Analysis in $\\mathbb{Z}^n$ and Applications to Integer Linear Programming","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3092190404","doi":"https://doi.org/10.1137/19m1281678","mag":"3092190404"},"language":"en","primary_location":{"id":"doi:10.1137/19m1281678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1281678","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/A5000941872","display_name":"Jun Li","orcid":"https://orcid.org/0000-0003-3435-4053"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jun Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084195707","display_name":"Giandomenico Mastroeni","orcid":"https://orcid.org/0000-0002-3848-1554"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giandomenico Mastroeni","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000941872"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2945,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53075823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"4","first_page":"2809","last_page":"2840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"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":0.998199999332428,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9950000047683716,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9936000108718872,"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":0.8104612827301025},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.6570086479187012},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5501046776771545},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5435481071472168},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5292356014251709},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5111759305000305},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4793742001056671},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3939468264579773},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32460370659828186},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0945843756198883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09003770351409912}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8104612827301025},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6570086479187012},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5501046776771545},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5435481071472168},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5292356014251709},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5111759305000305},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4793742001056671},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3939468264579773},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32460370659828186},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0945843756198883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09003770351409912},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1281678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1281678","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"},{"id":"pmh:oai:arpi.unipi.it:11568/1066086","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/1066086","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2084943018","display_name":null,"funder_award_id":"17YC379","funder_id":"https://openalex.org/F4320324420","funder_display_name":"China West Normal University"},{"id":"https://openalex.org/G4418444371","display_name":null,"funder_award_id":"11871059","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6264965186","display_name":null,"funder_award_id":"16TD0019","funder_id":"https://openalex.org/F4320322970","funder_display_name":"Education Department of Sichuan Province"},{"id":"https://openalex.org/G6347830153","display_name":null,"funder_award_id":"11371015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322970","display_name":"Education Department of Sichuan Province","ror":"https://ror.org/05s1c4z27"},{"id":"https://openalex.org/F4320324420","display_name":"China West Normal University","ror":"https://ror.org/04s99y476"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2009683816","https://openalex.org/W2035186046","https://openalex.org/W2049688189","https://openalex.org/W2063885213","https://openalex.org/W2066037950","https://openalex.org/W2096154249","https://openalex.org/W2123812125","https://openalex.org/W2287476638","https://openalex.org/W2325671244","https://openalex.org/W2329440662","https://openalex.org/W2598386307","https://openalex.org/W4297069203"],"related_works":["https://openalex.org/W1925942709","https://openalex.org/W2047683846","https://openalex.org/W2044902158","https://openalex.org/W2109912052","https://openalex.org/W1711527768","https://openalex.org/W4285278887","https://openalex.org/W2365237642","https://openalex.org/W2995925505","https://openalex.org/W3116484972","https://openalex.org/W2941986668"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,56,71],"compare":[4],"the":[5,58,92,104],"definitions":[6,31],"of":[7,32],"convex":[8,11,33,36,46,48,53,61],"sets":[9,34,62],"and":[10,21,24,35,52,55,82],"functions":[12,37,54],"in":[13,63],"finite":[14,64],"dimensional":[15,65],"integer":[16,66,74],"spaces":[17],"introduced":[18],"by":[19,90],"Adivar":[20],"Fang,":[22],"Borwein,":[23],"Giladi,":[25],"respectively.":[26],"We":[27,40,96],"show":[28],"that":[29],"their":[30],"are":[38],"equivalent.":[39],"also":[41],"provide":[42,98],"exact":[43],"formulations":[44],"for":[45],"sets,":[47,51],"cones,":[49],"affine":[50],"analyze":[57],"separation":[59],"between":[60],"spaces.":[67],"As":[68],"an":[69,73],"application,":[70],"consider":[72],"linear":[75,79],"programming":[76],"problem":[77],"with":[78],"inequality":[80],"constraints":[81],"obtain":[83],"some":[84,99],"necessary":[85],"or":[86],"sufficient":[87],"optimality":[88,106],"conditions":[89],"employing":[91],"image":[93],"space":[94],"analysis.":[95],"finally":[97],"computational":[100],"results":[101],"based":[102],"on":[103],"above-mentioned":[105],"conditions.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}