{"id":"https://openalex.org/W4394847492","doi":"https://doi.org/10.1137/22m1531257","title":"Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation","display_name":"Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation","publication_year":2024,"publication_date":"2024-04-16","ids":{"openalex":"https://openalex.org/W4394847492","doi":"https://doi.org/10.1137/22m1531257"},"language":"en","primary_location":{"id":"doi:10.1137/22m1531257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1531257","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/A5101945211","display_name":"Jie Wang","orcid":"https://orcid.org/0000-0002-9681-1451"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Wang","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101945211"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":0.765,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62177402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"34","issue":"2","first_page":"1490","last_page":"1514"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987999796867371,"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/T11236","display_name":"Control Systems and Identification","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.847527265548706},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6694509387016296},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5682497024536133},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5113508105278015},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4995851516723633},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.47619903087615967},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41853630542755127},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.405295193195343},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19231203198432922},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10252252221107483}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.847527265548706},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6694509387016296},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5682497024536133},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5113508105278015},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4995851516723633},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47619903087615967},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41853630542755127},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.405295193195343},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19231203198432922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10252252221107483},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1531257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1531257","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/G7864953252","display_name":null,"funder_award_id":"12201618","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1568307856","https://openalex.org/W1596877211","https://openalex.org/W1982292900","https://openalex.org/W2009923109","https://openalex.org/W2016505313","https://openalex.org/W2029424027","https://openalex.org/W2069234357","https://openalex.org/W2114279577","https://openalex.org/W2138677859","https://openalex.org/W2611807022","https://openalex.org/W2620334136","https://openalex.org/W2963917343","https://openalex.org/W2963929326","https://openalex.org/W2971846693","https://openalex.org/W2997540580","https://openalex.org/W3008048690","https://openalex.org/W3040772724","https://openalex.org/W3094912491","https://openalex.org/W3105306379","https://openalex.org/W3113334666","https://openalex.org/W3142079985"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1585007175","https://openalex.org/W2371409811","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W4300101996","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W2956921597"],"abstract_inverted_index":{".We":[0],"study":[1],"optimal":[2,39,68,96],"simple":[3,40,69,97],"second-order":[4,11,41,70,98],"cone":[5,12,42,71,99,117],"representations":[6,43],"(a":[7],"particular":[8],"subclass":[9],"of":[10,38,49,66],"representations)":[13],"for":[14],"weighted":[15,51],"geometric":[16,52,113],"means,":[17],"which":[18],"turns":[19],"out":[20],"to":[21,25,61,77,92,103],"be":[22],"closely":[23],"related":[24],"minimum":[26],"mediated":[27,56,115],"sets.":[28],"Several":[29],"lower":[30],"bounds":[31,34],"and":[32,73,87,108],"upper":[33],"on":[35],"the":[36,47,63,81],"size":[37,65],"are":[44,59,90,111],"proved.":[45],"In":[46,80],"case":[48],"bivariate":[50],"means":[53],"(equivalently,":[54],"one-dimensional":[55],"sets),":[57],"we":[58],"able":[60],"prove":[62],"exact":[64],"an":[67,75,94],"representation":[72],"give":[74],"algorithm":[76],"compute":[78,93],"one.":[79],"genenal":[82],"case,":[83],"fast":[84],"heuristic":[85],"algorithms":[86,89],"traversal":[88],"proposed":[91],"approximately":[95],"representation.":[100],"Finally,":[101],"applications":[102],"polynomial":[104],"optimization,":[105,107],"matrix":[106],"quantum":[109],"information":[110],"provided.Keywordsweighted":[112],"meanminimum":[114],"setsecond-order":[116],"representationpolynomial":[118],"optimizationsemidefinite":[119],"representationMSC":[120],"codes90C2590C2290C23":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
