{"id":"https://openalex.org/W2088163136","doi":"https://doi.org/10.1109/cdc.2013.6761089","title":"Convexification of Generalized Network Flow problem with application to power systems","display_name":"Convexification of Generalized Network Flow problem with application to power systems","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2088163136","doi":"https://doi.org/10.1109/cdc.2013.6761089","mag":"2088163136"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6761089","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6761089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-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/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":true,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":["Department of Computing and Mathematical Sciences, California Institute of Technology","Dept. of Comput. & Math. Sci., California Inst. of Technol., Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computing and Mathematical Sciences, California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Dept. of Comput. & Math. Sci., California Inst. of Technol., Pasadena, CA, USA","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":["Department of Electrical Engineering, Columbia University","Dept. of Electr. Eng, Columbia Univ., New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Dept. of Electr. Eng, Columbia Univ., New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072786751"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":1.44594496,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86014634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"7552","last_page":"7559"},"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":0.9848999977111816,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9775000214576721,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6708477735519409},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6094047427177429},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5351356863975525},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5168409943580627},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.49984002113342285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4950024485588074},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.47666338086128235},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47075703740119934},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46836864948272705},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.44584476947784424},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.44207918643951416},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.43517470359802246},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.43147075176239014},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4236510694026947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3731558918952942},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3240453004837036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07903605699539185}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6708477735519409},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6094047427177429},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5351356863975525},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5168409943580627},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.49984002113342285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4950024485588074},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.47666338086128235},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47075703740119934},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46836864948272705},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.44584476947784424},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.44207918643951416},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.43517470359802246},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.43147075176239014},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4236510694026947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3731558918952942},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3240453004837036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07903605699539185},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2013.6761089","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6761089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W391867494","https://openalex.org/W1507082306","https://openalex.org/W1552561242","https://openalex.org/W1876349971","https://openalex.org/W1964119857","https://openalex.org/W1964577612","https://openalex.org/W1977545325","https://openalex.org/W1990137274","https://openalex.org/W1993496017","https://openalex.org/W2000247330","https://openalex.org/W2010997912","https://openalex.org/W2014035031","https://openalex.org/W2045068465","https://openalex.org/W2051290577","https://openalex.org/W2062451421","https://openalex.org/W2077230226","https://openalex.org/W2088163136","https://openalex.org/W2091260897","https://openalex.org/W2095570364","https://openalex.org/W2102674521","https://openalex.org/W2104106131","https://openalex.org/W2104255928","https://openalex.org/W2111416445","https://openalex.org/W2111653328","https://openalex.org/W2120086273","https://openalex.org/W2122700623","https://openalex.org/W2128166312","https://openalex.org/W2134172715","https://openalex.org/W2134869843","https://openalex.org/W2141380252","https://openalex.org/W2145367961","https://openalex.org/W2147665001","https://openalex.org/W2149342630","https://openalex.org/W2158040846","https://openalex.org/W2165775468","https://openalex.org/W2166541787","https://openalex.org/W2296319761","https://openalex.org/W4213060235","https://openalex.org/W4250589301","https://openalex.org/W4292691059","https://openalex.org/W6633211032","https://openalex.org/W6678926812","https://openalex.org/W6681415697"],"related_works":["https://openalex.org/W3141113327","https://openalex.org/W2080904092","https://openalex.org/W3035974271","https://openalex.org/W3161514703","https://openalex.org/W3207627914","https://openalex.org/W2270959725","https://openalex.org/W2151525839","https://openalex.org/W648253840","https://openalex.org/W2051329268","https://openalex.org/W2092572272"],"abstract_inverted_index":{"This":[0,54,95],"paper":[1],"is":[2,19,61,87,149,216],"concerned":[3],"with":[4,21],"the":[5,71,79,92,104,141,158,206,210,230,239],"minimum-cost":[6],"flow":[7,12,59,80,161],"problem":[8,163,169],"over":[9,152],"an":[10,113,250],"arbitrary":[11],"network.":[13],"In":[14],"this":[15,147,167,200],"problem,":[16,55],"each":[17,26,37],"node":[18],"associated":[20],"some":[22],"possibly":[23],"unknown":[24,30],"injection,":[25],"line":[27],"has":[28,164],"two":[29,179,203],"flows":[31,47,102,109,138],"at":[32],"its":[33,66],"ends":[34],"related":[35],"to":[36,49,65,99,108,112,132,140,194,234],"other":[38,127],"via":[39],"a":[40,84,134,222,236],"nonlinear":[41,67],"function,":[42],"and":[43,46,76,81,189,227],"all":[44],"injections":[45,107,121,241],"need":[48],"satisfy":[50],"certain":[51],"box":[52],"constraints.":[53,69,196],"named":[56],"generalized":[57],"network":[58],"(GNF),":[60],"highly":[62],"non-convex":[63,168],"due":[64],"equality":[68],"Under":[70],"practical":[72],"assumption":[73],"of":[74,78,116,137,146,199],"monotonicity":[75],"convexity":[77],"cost":[82],"functions,":[83],"convex":[85],"relaxation":[86,96,232],"proposed,":[88],"which":[89],"always":[90],"finds":[91],"optimal":[93,101,120,159,240],"injections.":[94,142],"may":[97,245],"fail":[98],"find":[100,133,235],"because":[103],"mapping":[105],"from":[106,249],"might":[110],"lead":[111],"exponential":[114],"number":[115],"solutions.":[117],"However,":[118],"once":[119],"are":[122],"found":[123],"in":[124,150,219],"polynomial":[125],"time,":[126],"techniques":[128],"can":[129,170],"be":[130,171,247],"used":[131],"feasible":[135],"set":[136],"corresponding":[139],"A":[143],"primary":[144],"application":[145],"work":[148,156,201],"optimization":[151],"power":[153,160,191],"networks.":[154],"Recent":[155],"on":[157],"(OPF)":[162],"shown":[165],"that":[166],"solved":[172],"efficiently":[173],"using":[174],"semidefinite":[175],"programming":[176],"(SDP)":[177],"after":[178],"approximations:":[180],"relaxing":[181,190],"angle":[182,225],"constraints":[183],"(by":[184],"adding":[185],"virtual":[186],"phase":[187],"shifters)":[188],"balance":[192,214],"equations":[193],"inequality":[195],"The":[197],"results":[198],"prove":[202],"facts":[204],"for":[205],"OPF":[207],"problem:":[208],"(i)":[209],"second":[211],"approximation":[212],"(on":[213],"equations)":[215],"not":[217,243],"needed":[218],"practice":[220],"under":[221],"very":[223],"mild":[224],"assumption,":[226],"(ii)":[228],"if":[229],"SDP":[231],"fails":[233],"rank-one":[237],"solution,":[238],"(and":[242],"flows)":[244],"still":[246],"recovered":[248],"undesirable":[251],"high-rank":[252],"solution.":[253]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}