{"id":"https://openalex.org/W2109375302","doi":"https://doi.org/10.1109/acssc.2013.6810520","title":"Convex relaxation for optimal power flow problem: Mesh networks","display_name":"Convex relaxation for optimal power flow problem: Mesh networks","publication_year":2013,"publication_date":"2013-11-01","ids":{"openalex":"https://openalex.org/W2109375302","doi":"https://doi.org/10.1109/acssc.2013.6810520","mag":"2109375302"},"language":"en","primary_location":{"id":"doi:10.1109/acssc.2013.6810520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acssc.2013.6810520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Asilomar Conference on Signals, Systems and Computers","raw_type":"proceedings-article"},"type":"conference-paper","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/A5015341130","display_name":"Ramtin Madani","orcid":"https://orcid.org/0000-0001-9246-2357"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramtin Madani","raw_affiliation_strings":["Electrical Engineering Department, Columbia University","[Electrical Engineering Department, Columbia University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Columbia University","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"[Electrical Engineering Department, Columbia University]","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072786751","display_name":"Somayeh Sojoudi","orcid":"https://orcid.org/0000-0001-7177-7712"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":["Department of Computing & Mathematical Sciences, California Institute of Technology","Department of Computing and Mathematical Sciences; California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing & Mathematical Sciences, California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Department of Computing and Mathematical Sciences; California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042580848","display_name":"Javad Lavaei","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javad Lavaei","raw_affiliation_strings":["Electrical Engineering Department, Columbia University","[Electrical Engineering Department, Columbia University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Columbia University","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"[Electrical Engineering Department, Columbia University]","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1375","last_page":"1382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9997000098228455,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9997000098228455,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9836999773979187,"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9811000227928162,"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/relaxation","display_name":"Relaxation (psychology)","score":0.7167091369628906},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6673794984817505},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.651749312877655},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6314038634300232},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5335671901702881},{"id":"https://openalex.org/keywords/lossless-compression","display_name":"Lossless compression","score":0.47793060541152954},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4686046838760376},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.45474880933761597},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4484262764453888},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4449484348297119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44271838665008545},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4359838366508484},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3916120231151581},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22901633381843567},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11310064792633057},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.08864620327949524}],"concepts":[{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.7167091369628906},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6673794984817505},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.651749312877655},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6314038634300232},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5335671901702881},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.47793060541152954},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4686046838760376},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.45474880933761597},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4484262764453888},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4449484348297119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44271838665008545},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4359838366508484},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3916120231151581},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22901633381843567},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11310064792633057},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.08864620327949524},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/acssc.2013.6810520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acssc.2013.6810520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Asilomar Conference on Signals, Systems and Computers","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.702.7844","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.702.7844","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ieor.berkeley.edu/%7Elavaei/OPF_Mesh_Apr_2013.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.703.1307","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.703.1307","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ieor.berkeley.edu/%7Elavaei/Penalized_SDP_2013.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W391867494","https://openalex.org/W428203260","https://openalex.org/W571085588","https://openalex.org/W1876349971","https://openalex.org/W1968878112","https://openalex.org/W2036681141","https://openalex.org/W2062451421","https://openalex.org/W2091260897","https://openalex.org/W2103136320","https://openalex.org/W2104106131","https://openalex.org/W2111416445","https://openalex.org/W2111653328","https://openalex.org/W2122700623","https://openalex.org/W2134172715","https://openalex.org/W2134869843","https://openalex.org/W2141380252","https://openalex.org/W2147665001","https://openalex.org/W2231838537","https://openalex.org/W4300044162","https://openalex.org/W6676811001"],"related_works":["https://openalex.org/W2885220786","https://openalex.org/W2962729054","https://openalex.org/W1964031338","https://openalex.org/W1997135619","https://openalex.org/W2952885210","https://openalex.org/W2893860505","https://openalex.org/W2963842491","https://openalex.org/W4289490443","https://openalex.org/W2934635345","https://openalex.org/W2109375302"],"abstract_inverted_index":{"This":[0,14],"paper":[1],"is":[2,21,52,69,104,110,125,132,141,150,157,185,199],"concerned":[3],"with":[4,98],"a":[5,44,56,161,169,182,189],"fundamental":[6],"resource":[7],"allocation":[8],"problem":[9],"for":[10,61,87,143,160,192],"electrical":[11],"power":[12,18],"networks.":[13,76,92],"problem,":[15],"named":[16],"optimal":[17],"flow":[19],"(OPF),":[20],"nonconvex":[22],"due":[23],"to":[24,54,71,187],"the":[25,29,81,84,107,113,118,122,128,136,154,176,179,193,197],"nonlinearities":[26],"imposed":[27],"by":[28],"laws":[30],"of":[31,59,83,100,121,139,146,178],"physics,":[32],"and":[33,65,116],"has":[34],"been":[35],"studied":[36],"since":[37],"1962.":[38],"We":[39],"have":[40,168],"recently":[41],"shown":[42,105,151],"that":[43,106,117,135,152],"convex":[45,111,126],"relaxation":[46,86,138,156,195,198],"based":[47],"on":[48,175],"semidefinite":[49],"programming":[50],"(SDP)":[51],"able":[53],"find":[55],"global":[57],"solution":[58,171,191],"OPF":[60,88,140],"IEEE":[62],"benchmark":[63],"systems,":[64],"moreover":[66],"this":[67,144],"technique":[68],"guaranteed":[70],"work":[72,79],"over":[73,89],"acyclic":[74],"(distribution)":[75],"The":[77],"present":[78],"studies":[80],"potential":[82],"SDP":[85,137,155,194],"cyclic":[90],"(transmission)":[91],"Given":[93],"an":[94],"arbitrary":[95],"weakly-cyclic":[96],"network":[97],"cycles":[99],"size":[101],"3,":[102],"it":[103,149,165],"injection":[108,123],"region":[109,124],"in":[112,127],"lossless":[114],"case":[115],"Pareto":[119],"front":[120],"lossy":[129],"case.":[130],"It":[131],"also":[133],"proved":[134],"exact":[142,159],"type":[145],"network.":[147,180],"Moreover,":[148],"if":[153],"not":[158,200],"general":[162],"mesh":[163],"network,":[164],"would":[166],"still":[167],"low-rank":[170],"whose":[172],"rank":[173],"depends":[174],"structure":[177],"Finally,":[181],"heuristic":[183],"method":[184],"proposed":[186],"recover":[188],"rank-1":[190],"whenever":[196],"exact.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}