{"id":"https://openalex.org/W2050328660","doi":"https://doi.org/10.1137/s1052623499358689","title":"Approximate Max-Min Resource Sharing for Structured Concave Optimization","display_name":"Approximate Max-Min Resource Sharing for Structured Concave Optimization","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2050328660","doi":"https://doi.org/10.1137/s1052623499358689","mag":"2050328660"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623499358689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623499358689","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":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3271378","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084098678","display_name":"Michael D. Grigoriadis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. D. Grigoriadis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110428486","display_name":"Leonid Khachiyan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. G. Khachiyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033762785","display_name":"Lorant Porkolab","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Porkolab","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030121703","display_name":"Jorge Villavicencio","orcid":"https://orcid.org/0000-0002-2523-6584"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Villavicencio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3079,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.88518402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"1081","last_page":"1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983000159263611,"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":0.82383131980896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6570037007331848},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6048165559768677},{"id":"https://openalex.org/keywords/concave-function","display_name":"Concave function","score":0.5548280477523804},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5513144731521606},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5314297676086426},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5018737316131592},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4789593517780304},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.47455960512161255},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4134117066860199},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4117836058139801},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3814805746078491},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3338509798049927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10560905933380127},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06968435645103455}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.82383131980896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6570037007331848},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6048165559768677},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.5548280477523804},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5513144731521606},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5314297676086426},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5018737316131592},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4789593517780304},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47455960512161255},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4134117066860199},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4117836058139801},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3814805746078491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3338509798049927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10560905933380127},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06968435645103455},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1052623499358689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623499358689","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:americanae.aecid.es:3271378","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3271378","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON OPTIMIZATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/172852","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/172852","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON OPTIMIZATION","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3271378","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3271378","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON OPTIMIZATION","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W122708907","https://openalex.org/W330591652","https://openalex.org/W1632601927","https://openalex.org/W1903526182","https://openalex.org/W1980869082","https://openalex.org/W1993161326","https://openalex.org/W2053924317","https://openalex.org/W2064948689","https://openalex.org/W2066883826","https://openalex.org/W2070426678","https://openalex.org/W2087338175","https://openalex.org/W2134422938","https://openalex.org/W2165956524","https://openalex.org/W4235328454","https://openalex.org/W4240034232","https://openalex.org/W4254960878"],"related_works":["https://openalex.org/W3044475370","https://openalex.org/W4241145077","https://openalex.org/W2387950976","https://openalex.org/W4387870386","https://openalex.org/W3153752017","https://openalex.org/W2808215963","https://openalex.org/W217463380","https://openalex.org/W1561462659","https://openalex.org/W2905418717","https://openalex.org/W2001828069"],"abstract_inverted_index":{"We":[0,33],"present":[1],"a":[2,29,44,90],"Lagrangian":[3],"decomposition":[4],"algorithm":[5,37],"which":[6,48,99],"uses":[7],"logarithmic":[8],"potential":[9],"reduction":[10],"to":[11,52],"compute":[12],"an":[13,84],"$\\varepsilon$-approximate":[14],"solution":[15,92],"of":[16,69,86,93],"the":[17,62,67],"general":[18],"max-min":[19],"resource":[20],"sharing":[21],"problem":[22],"with":[23],"M":[24],"nonnegative":[25],"concave":[26],"constraints":[27],"on":[28],"convex":[30,71],"set":[31],"B.":[32],"show":[34],"that":[35],"this":[36],"runs":[38],"in":[39,103],"$O(M(\\varepsilon^{-2}+{\\rm":[40],"ln}":[41],"M))$":[42],"iterations,":[43],"data":[45],"independent":[46,95],"bound":[47],"is":[49,66,78],"optimal":[50],"up":[51],"polylogarithmic":[53],"factors":[54],"for":[55],"any":[56],"fixed":[57],"relative":[58],"accuracy":[59],"$\\varepsilon\\in(0,1)$.":[60],"In":[61],"block-angular":[63],"case,":[64],"B":[65],"product":[68],"K":[70,94],"sets":[72],"(blocks)":[73],"and":[74],"each":[75],"constraint":[76],"function":[77],"block":[79,96],"separable.":[80],"For":[81],"such":[82],"models,":[83],"iteration":[85],"our":[87],"method":[88],"requires":[89],"$\\Theta(\\varepsilon)$-approximate":[91],"maximization":[97],"problems":[98],"can":[100],"be":[101],"computed":[102],"parallel.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
