{"id":"https://openalex.org/W2290646310","doi":"https://doi.org/10.1109/cdc.2015.7403257","title":"Inverse function theorem for polynomial equations using semidefinite programming","display_name":"Inverse function theorem for polynomial equations using semidefinite programming","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2290646310","doi":"https://doi.org/10.1109/cdc.2015.7403257","mag":"2290646310"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7403257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403257","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","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/A5035440978","display_name":"Morteza Ashraphijuo","orcid":"https://orcid.org/0000-0001-9324-620X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Morteza Ashraphijuo","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","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":["Department of Electrical Engineering, Columbia University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042580848","display_name":"Javad Lavaei","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javad Lavaei","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035440978"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":2.9589,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91404825,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"6589","last_page":"6596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9984999895095825,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9890000224113464,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.7263637781143188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7184821367263794},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.604836642742157},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5559864044189453},{"id":"https://openalex.org/keywords/inverse-function","display_name":"Inverse function","score":0.5387516617774963},{"id":"https://openalex.org/keywords/inverse-function-theorem","display_name":"Inverse function theorem","score":0.503309428691864},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.4537610411643982},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4478349983692169},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4424424171447754},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4423191249370575},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4364498555660248},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.4271584451198578},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40894579887390137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29649651050567627},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.23441028594970703},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17183664441108704},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.12129124999046326},{"id":"https://openalex.org/keywords/picard\u2013lindel\u00f6f-theorem","display_name":"Picard\u2013Lindel\u00f6f theorem","score":0.10526296496391296}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7263637781143188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7184821367263794},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.604836642742157},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5559864044189453},{"id":"https://openalex.org/C140528856","wikidata":"https://www.wikidata.org/wiki/Q191884","display_name":"Inverse function","level":3,"score":0.5387516617774963},{"id":"https://openalex.org/C43987214","wikidata":"https://www.wikidata.org/wiki/Q931001","display_name":"Inverse function theorem","level":4,"score":0.503309428691864},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.4537610411643982},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4478349983692169},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4424424171447754},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4423191249370575},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4364498555660248},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.4271584451198578},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40894579887390137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29649651050567627},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.23441028594970703},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17183664441108704},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.12129124999046326},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.10526296496391296},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.1109/cdc.2015.7403257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403257","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","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":26,"referenced_works":["https://openalex.org/W1632601927","https://openalex.org/W1967344706","https://openalex.org/W1985123706","https://openalex.org/W1996215314","https://openalex.org/W2001613283","https://openalex.org/W2007104311","https://openalex.org/W2031494345","https://openalex.org/W2034188706","https://openalex.org/W2045148236","https://openalex.org/W2078397124","https://openalex.org/W2079135578","https://openalex.org/W2080362883","https://openalex.org/W2085523940","https://openalex.org/W2136290775","https://openalex.org/W2138118438","https://openalex.org/W2141380252","https://openalex.org/W2154394329","https://openalex.org/W2155724501","https://openalex.org/W2160766917","https://openalex.org/W2611328865","https://openalex.org/W3143305990","https://openalex.org/W3148325197","https://openalex.org/W3210839039","https://openalex.org/W4236167420","https://openalex.org/W4250589301","https://openalex.org/W6683470859"],"related_works":["https://openalex.org/W162626055","https://openalex.org/W1802683367","https://openalex.org/W4293417932","https://openalex.org/W2247514228","https://openalex.org/W1983886663","https://openalex.org/W4388321791","https://openalex.org/W3030418996","https://openalex.org/W2028301507","https://openalex.org/W2347049040","https://openalex.org/W4229020201"],"abstract_inverted_index":{"This":[0,121],"paper":[1],"is":[2,30,163,171],"concerned":[3],"with":[4,174],"obtaining":[5],"the":[6,25,28,32,38,41,49,79,86,97,105,108,134,155,178],"inverse":[7,33,39,59,80,106,135],"of":[8,27,40,48,76,85,99,107,146,154],"polynomial":[9,17,42,109,147],"functions":[10],"using":[11,65],"semidefinite":[12],"programming":[13],"(SDP).":[14],"Given":[15],"a":[16,20,46,83,92,116,138],"function":[18,29,34,43,60,81,110,136],"and":[19,115,177],"nominal":[21,50,87,113],"point":[22],"at":[23,45,82,111],"which":[24,77],"Jacobian":[26],"invertible,":[31],"theorem":[35],"states":[36],"that":[37,57,103,132],"exists":[44],"neighborhood":[47,84,117],"point.":[51,88,120],"In":[52],"this":[53,58,169],"work,":[54],"we":[55,70],"show":[56],"can":[61,149],"be":[62,150],"found":[63],"locally":[64],"convex":[66,93],"optimization.":[67],"More":[68],"precisely,":[69],"propose":[71],"infinitely":[72],"many":[73],"SDPs,":[74],"each":[75,119],"finds":[78,104,133],"We":[89],"also":[90],"design":[91],"optimization":[94],"to":[95,125],"check":[96],"existence":[98],"an":[100,127,142,160],"SDP":[101,128,157],"problem":[102,129,158],"multiple":[112],"points":[114],"around":[118],"makes":[122],"it":[123],"possible":[124],"identify":[126],"(if":[130],"any)":[131],"over":[137],"large":[139],"region.":[140],"As":[141],"application,":[143],"any":[144],"system":[145],"equations":[148],"solved":[151],"by":[152],"means":[153],"proposed":[156],"whenever":[159],"approximate":[161],"solution":[162],"available.":[164],"The":[165],"method":[166,176],"developed":[167],"in":[168],"work":[170],"numerically":[172],"compared":[173],"Newton's":[175],"nuclear-norm":[179],"technique.":[180]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
