{"id":"https://openalex.org/W2755023938","doi":"https://doi.org/10.1137/16m1084328","title":"Duality in Countably Infinite Monotropic Programs","display_name":"Duality in Countably Infinite Monotropic Programs","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2755023938","doi":"https://doi.org/10.1137/16m1084328","mag":"2755023938"},"language":"en","primary_location":{"id":"doi:10.1137/16m1084328","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084328","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/A5068691426","display_name":"Archis Ghate","orcid":"https://orcid.org/0000-0001-6093-5340"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Archis Ghate","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068691426"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1421,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82677516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"3","first_page":"2010","last_page":"2033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9782999753952026,"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/countable-set","display_name":"Countable set","score":0.7900532484054565},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7174416184425354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7138264775276184},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5575921535491943},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5030936598777771},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.46923238039016724},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.46590954065322876},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.443327397108078},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.34860360622406006},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.34265467524528503},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34193649888038635},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.31005728244781494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2684040069580078},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14063423871994019}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7900532484054565},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7174416184425354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7138264775276184},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5575921535491943},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5030936598777771},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.46923238039016724},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.46590954065322876},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.443327397108078},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34860360622406006},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.34265467524528503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34193649888038635},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.31005728244781494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2684040069580078},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14063423871994019},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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:10.1137/16m1084328","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084328","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6399999856948853}],"awards":[{"id":"https://openalex.org/G2112085520","display_name":null,"funder_award_id":"CMMI 1561918","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W133224232","https://openalex.org/W1485732691","https://openalex.org/W1966091678","https://openalex.org/W2017649644","https://openalex.org/W2035320001","https://openalex.org/W2037249457","https://openalex.org/W2051994935","https://openalex.org/W2066957127","https://openalex.org/W2097415784","https://openalex.org/W2105260964","https://openalex.org/W2127533431","https://openalex.org/W2130495934","https://openalex.org/W2145072018","https://openalex.org/W2162748558","https://openalex.org/W2222363143","https://openalex.org/W2737963458","https://openalex.org/W2798735774","https://openalex.org/W4241474317","https://openalex.org/W4253576536","https://openalex.org/W4255867662"],"related_works":["https://openalex.org/W2325192077","https://openalex.org/W2010724422","https://openalex.org/W4233192371","https://openalex.org/W2016306996","https://openalex.org/W2423508375","https://openalex.org/W3216313338","https://openalex.org/W2000285254","https://openalex.org/W2950608892","https://openalex.org/W4299012739","https://openalex.org/W2963031829"],"abstract_inverted_index":{"Finite-dimensional":[0],"monotropic":[1,32,87,107],"programs":[2,26,33,53,88,108,191],"form":[3],"a":[4,133,165],"class":[5],"of":[6,60,167,171],"convex":[7,14,25,72],"optimization":[8],"problems":[9,18,41,76],"that":[10],"includes":[11],"linear":[12,28,52,96],"programs,":[13],"minimum":[15,73],"cost":[16,74],"flow":[17,75],"on":[19,77],"networks":[20,80],"and":[21,23,42,70,81,142,146,161],"hypernetworks,":[22],"separable":[24],"with":[27],"constraints.":[29],"Countably":[30],"infinite":[31,51,79,106,189],"arise,":[34],"for":[35,85,95,104],"example,":[36],"in":[37,43,117,132,177],"infinite-horizon":[38,61],"sequential":[39],"decision":[40,68],"robust":[44],"optimization.":[45],"Their":[46],"applications":[47],"encompass":[48],"(i)":[49],"countably":[50,78,105,188],"such":[54],"as":[55,63,65,90,92,194],"the":[56,99,129,137,172,178],"shortest":[57],"path":[58],"formulations":[59],"nonstationary":[62],"well":[64],"countable-state":[66],"Markov":[67],"processes;":[69],"(ii)":[71],"hypernetworks.":[82],"Duality":[83],"results":[84,103,186],"finite-dimensional":[86,152,168],"are":[89,109,149,175,180,192],"powerful":[91],"those":[93],"available":[94],"programs.":[97],"On":[98],"contrary,":[100],"applicable":[101],"duality":[102,145,159,163,185],"currently":[110],"nonexistent":[111],"owing":[112],"to":[113],"several":[114],"mathematical":[115,190],"pathologies":[116],"infinite-dimensional":[118,173],"sequence":[119,134,166],"spaces.":[120],"This":[121],"paper":[122],"overcomes":[123],"this":[124],"hurdle":[125],"by":[126],"first":[127],"embedding":[128],"dual":[130],"variables":[131],"space":[135],"where":[136],"Lagrangian":[138],"function":[139],"is":[140],"well-defined":[141],"finite.":[143],"Weak":[144],"complementary":[147],"slackness":[148],"derived":[150],"using":[151],"proof":[153],"techniques.":[154],"Conditions":[155],"under":[156],"which":[157],"zero":[158],"gaps":[160],"strong":[162],"between":[164],"primal-dual":[169],"projections":[170],"problem":[174],"preserved":[176],"limit":[179],"established.":[181],"Essentially":[182],"all":[183],"known":[184],"about":[187],"recovered":[193],"special":[195],"cases.":[196]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}