{"id":"https://openalex.org/W3016994994","doi":"https://doi.org/10.1137/18m1174805","title":"Duality Gap Estimation via a Refined Shapley--Folkman Lemma","display_name":"Duality Gap Estimation via a Refined Shapley--Folkman Lemma","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3016994994","doi":"https://doi.org/10.1137/18m1174805","mag":"3016994994"},"language":"en","primary_location":{"id":"doi:10.1137/18m1174805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1174805","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/A5057565845","display_name":"Yingjie Bi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yingjie Bi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090688439","display_name":"Ao Tang","orcid":"https://orcid.org/0000-0002-1126-3469"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ao Tang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057565845"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3112,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.55797033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"30","issue":"2","first_page":"1094","last_page":"1118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/lemma","display_name":"Lemma (botany)","score":0.6914875507354736},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.6773927211761475},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6610004901885986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6336662173271179},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5835037231445312},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5705965757369995},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.4946388900279999},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4940374493598938},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4779758155345917},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4222675561904907},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3955468237400055},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.38567471504211426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23553743958473206}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6914875507354736},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.6773927211761475},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6610004901885986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6336662173271179},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5835037231445312},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5705965757369995},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4946388900279999},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4940374493598938},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4779758155345917},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4222675561904907},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3955468237400055},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.38567471504211426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23553743958473206},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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:10.1137/18m1174805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1174805","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":[{"id":"https://openalex.org/G5368154739","display_name":null,"funder_award_id":"Jacobs Fellowship","funder_id":"https://openalex.org/F4320309624","funder_display_name":"Cornell University"},{"id":"https://openalex.org/G6873216588","display_name":null,"funder_award_id":"N00014-17-1-2419","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320309624","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1996820366","https://openalex.org/W2000354435","https://openalex.org/W2014579210","https://openalex.org/W2037515146","https://openalex.org/W2161272050","https://openalex.org/W2165786861","https://openalex.org/W2297878663"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W4285390085","https://openalex.org/W2801357573","https://openalex.org/W4387870386","https://openalex.org/W2114397143","https://openalex.org/W2000285254"],"abstract_inverted_index":{"Based":[0],"on":[1],"concepts":[2],"like":[3],"the":[4,21,30,46,54,66,74],"$k$th":[5],"convex":[6],"hull":[7],"and":[8,24,53],"finer":[9],"characterization":[10],"of":[11,13,20,33],"nonconvexity":[12],"a":[14,18,26],"function,":[15],"we":[16],"propose":[17],"refinement":[19],"Shapley--Folkman":[22],"lemma":[23],"derive":[25],"new":[27,67],"estimate":[28],"for":[29],"duality":[31],"gap":[32],"nonconvex":[34,86],"optimization":[35],"problems":[36],"with":[37,84],"separable":[38],"objective":[39],"functions.":[40],"We":[41],"apply":[42],"our":[43],"result":[44],"to":[45,63,82],"network":[47],"utility":[48],"maximization":[49],"problem":[50,58],"in":[51,59],"networking":[52],"dynamic":[55],"spectrum":[56],"management":[57],"communication":[60],"as":[61],"examples":[62],"demonstrate":[64],"that":[65],"bound":[68],"can":[69],"be":[70],"qualitatively":[71],"tighter":[72],"than":[73],"existing":[75],"ones.":[76],"The":[77],"idea":[78],"is":[79],"also":[80],"applicable":[81],"cases":[83],"general":[85],"constraints.":[87]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
