{"id":"https://openalex.org/W4297069203","doi":"https://doi.org/10.1007/bf02680565","title":"Discrete convex analysis","display_name":"Discrete convex analysis","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W4297069203","doi":"https://doi.org/10.1007/bf02680565"},"language":"en","primary_location":{"id":"doi:10.1007/bf02680565","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02680565","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/A5032957138","display_name":"Kazuo Murota","orcid":"https://orcid.org/0000-0003-1518-9152"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuo Murota","raw_affiliation_strings":["Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan"],"affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032957138"],"corresponding_institution_ids":["https://openalex.org/I22299242"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.0676,"has_fulltext":false,"cited_by_count":171,"citation_normalized_percentile":{"value":0.94598591,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"83","issue":"1-3","first_page":"313","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10374","display_name":"Advanced Graph Theory Research","score":0.996999979019165,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8345415592193604},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.7960275411605835},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.6366055011749268},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.6363469362258911},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.6180938482284546},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6142855286598206},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.5960742831230164},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5793144106864929},{"id":"https://openalex.org/keywords/quasiconvex-function","display_name":"Quasiconvex function","score":0.49915647506713867},{"id":"https://openalex.org/keywords/fenchels-duality-theorem","display_name":"Fenchel's duality theorem","score":0.48755306005477905},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47639527916908264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41732925176620483},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3829776346683502},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3683153986930847},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.35146626830101013},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.32021570205688477},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2771916389465332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8345415592193604},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.7960275411605835},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.6366055011749268},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.6363469362258911},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.6180938482284546},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6142855286598206},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.5960742831230164},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5793144106864929},{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.49915647506713867},{"id":"https://openalex.org/C32580822","wikidata":"https://www.wikidata.org/wiki/Q5443003","display_name":"Fenchel's duality theorem","level":5,"score":0.48755306005477905},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47639527916908264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41732925176620483},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3829776346683502},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3683153986930847},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.35146626830101013},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.32021570205688477},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2771916389465332},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02680565","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02680565","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W606453859","https://openalex.org/W1494436834","https://openalex.org/W1498671329","https://openalex.org/W1508474907","https://openalex.org/W1967702858","https://openalex.org/W1971775248","https://openalex.org/W1972946082","https://openalex.org/W1986638647","https://openalex.org/W1988684291","https://openalex.org/W1989262026","https://openalex.org/W1993531383","https://openalex.org/W2033329811","https://openalex.org/W2035186046","https://openalex.org/W2042275390","https://openalex.org/W2061647611","https://openalex.org/W2066894529","https://openalex.org/W2068200970","https://openalex.org/W2082976908","https://openalex.org/W2084330914","https://openalex.org/W2094571546","https://openalex.org/W2107504654","https://openalex.org/W2125690626","https://openalex.org/W2130529283","https://openalex.org/W2137468109","https://openalex.org/W2155370486","https://openalex.org/W2161413792","https://openalex.org/W2505968561","https://openalex.org/W2990145906","https://openalex.org/W2990955569","https://openalex.org/W4210391498","https://openalex.org/W4234130962","https://openalex.org/W4249667877","https://openalex.org/W4250204379","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W1687657632","https://openalex.org/W4220928172","https://openalex.org/W4210245775","https://openalex.org/W2384039353","https://openalex.org/W2029896594","https://openalex.org/W2345066843","https://openalex.org/W3213165575","https://openalex.org/W2351130384","https://openalex.org/W1983749636","https://openalex.org/W2136200239"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
