{"id":"https://openalex.org/W4296926842","doi":"https://doi.org/10.1561/2400000009","title":"Low-Rank Semidefinite Programming: Theory and Applications","display_name":"Low-Rank Semidefinite Programming: Theory and Applications","publication_year":2016,"publication_date":"2016-08-04","ids":{"openalex":"https://openalex.org/W4296926842","doi":"https://doi.org/10.1561/2400000009"},"language":"en","primary_location":{"id":"doi:10.1561/2400000009","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2400000009","pdf_url":null,"source":{"id":"https://openalex.org/S4210187074","display_name":"Foundations and Trends\u00ae in Optimization","issn_l":"2167-3888","issn":["2167-3888","2167-3918"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in 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/A5056003179","display_name":"Alex Lemon","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alex Lemon","raw_affiliation_strings":["Stanford University","Stanford University, USA"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105881332","display_name":"Anthony Man\u2013Cho So","orcid":"https://orcid.org/0000-0003-2588-7851"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Anthony Man-Cho So","raw_affiliation_strings":["The Chinese University of Hong Kong","The Chinese University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041526408","display_name":"Yinyu Ye","orcid":"https://orcid.org/0009-0001-3239-2622"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yinyu Ye","raw_affiliation_strings":["Stanford University","Stanford University, USA"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056003179"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":5.6579,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.9618336,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2","issue":"1-2","first_page":"1","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9846000075340271,"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":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.8508409261703491},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.8133196830749512},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6132189035415649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46077460050582886},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3922249674797058},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3734584450721741},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.27058976888656616},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22931182384490967},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.0825577974319458}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8508409261703491},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.8133196830749512},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6132189035415649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46077460050582886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3922249674797058},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3734584450721741},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.27058976888656616},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22931182384490967},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.0825577974319458}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1561/2400000009","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2400000009","pdf_url":null,"source":{"id":"https://openalex.org/S4210187074","display_name":"Foundations and Trends\u00ae in Optimization","issn_l":"2167-3888","issn":["2167-3888","2167-3918"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W116606405","https://openalex.org/W1560153690","https://openalex.org/W1604432248","https://openalex.org/W1606052501","https://openalex.org/W1968745099","https://openalex.org/W1979603710","https://openalex.org/W1984149403","https://openalex.org/W1984355469","https://openalex.org/W1985123706","https://openalex.org/W1986865581","https://openalex.org/W1994666506","https://openalex.org/W1999032440","https://openalex.org/W2000602248","https://openalex.org/W2005102197","https://openalex.org/W2005136695","https://openalex.org/W2014431362","https://openalex.org/W2030449718","https://openalex.org/W2038210983","https://openalex.org/W2042032299","https://openalex.org/W2049371785","https://openalex.org/W2050897335","https://openalex.org/W2051306216","https://openalex.org/W2052970196","https://openalex.org/W2053940560","https://openalex.org/W2056641273","https://openalex.org/W2057624533","https://openalex.org/W2059225841","https://openalex.org/W2063185045","https://openalex.org/W2063549526","https://openalex.org/W2063690908","https://openalex.org/W2068484625","https://openalex.org/W2068728923","https://openalex.org/W2069493373","https://openalex.org/W2074859470","https://openalex.org/W2075184363","https://openalex.org/W2078409719","https://openalex.org/W2087038607","https://openalex.org/W2092377825","https://openalex.org/W2093790790","https://openalex.org/W2100541427","https://openalex.org/W2103111465","https://openalex.org/W2106993652","https://openalex.org/W2108927308","https://openalex.org/W2109357213","https://openalex.org/W2110540077","https://openalex.org/W2111135554","https://openalex.org/W2113432563","https://openalex.org/W2117198760","https://openalex.org/W2118550318","https://openalex.org/W2122744491","https://openalex.org/W2128757878","https://openalex.org/W2129131372","https://openalex.org/W2133184112","https://openalex.org/W2138505091","https://openalex.org/W2140214428","https://openalex.org/W2141380252","https://openalex.org/W2143075842","https://openalex.org/W2144963972","https://openalex.org/W2145367961","https://openalex.org/W2145486800","https://openalex.org/W2146489710","https://openalex.org/W2152088446","https://openalex.org/W2159935945","https://openalex.org/W2162678712","https://openalex.org/W2164452299","https://openalex.org/W2167245803","https://openalex.org/W2167628558","https://openalex.org/W2401610261","https://openalex.org/W2502655619","https://openalex.org/W2912522929","https://openalex.org/W3003775594","https://openalex.org/W4250589301","https://openalex.org/W4250955649","https://openalex.org/W4291236916"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2386048074","https://openalex.org/W2572095861"],"abstract_inverted_index":{"Finding":[0],"low-rank":[1,55,66,71,77],"solutions":[2],"of":[3,19,39,54,64,84],"semidefinite":[4,13,28,41,56],"programs":[5,14],"is":[6,43],"important":[7],"in":[8],"many":[9],"applications.":[10],"For":[11],"example,":[12],"that":[15,60],"arise":[16],"as":[17],"relaxations":[18,25],"polynomial":[20],"optimization":[21],"problems":[22,89],"are":[23],"exact":[24],"when":[26],"the":[27,52,62,85],"program":[29,42],"has":[30],"a":[31,36,40,65],"rank-1":[32],"solution.":[33],"Unfortunately,":[34],"computing":[35,70],"minimum-rank":[37],"solution":[38],"an":[44],"NP-hard":[45],"problem.":[46],"In":[47],"this":[48],"paper":[49],"we":[50,81],"review":[51],"theory":[53,86],"programming,":[57],"presenting":[58],"theorems":[59],"guarantee":[61],"existence":[63],"solution,":[67],"heuristics":[68],"for":[69,75],"solutions,":[72],"and":[73,90],"algorithms":[74],"finding":[76],"approximate":[78],"solutions.":[79],"Then":[80],"present":[82],"applications":[83],"to":[87],"trust-region":[88],"signal":[91],"processing.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-31T06:02:25.137627","created_date":"2025-10-10T00:00:00"}
