{"id":"https://openalex.org/W81570845","doi":null,"title":"A Riemannian approach to large-scale constrained least-squares with symmetries","display_name":"A Riemannian approach to large-scale constrained least-squares with symmetries","publication_year":2014,"publication_date":"2014-10-20","ids":{"openalex":"https://openalex.org/W81570845","mag":"81570845"},"language":"en","primary_location":{"id":"pmh:oai:orbi.ulg.ac.be:2268/173257","doi":null,"is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/173257","pdf_url":"https://orbi.uliege.be/handle/2268/173257","source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"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":null,"raw_type":"http://purl.org/coar/resource_type/c_db06"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbi.uliege.be/handle/2268/173257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023551959","display_name":"Bamdev Mishra","orcid":"https://orcid.org/0000-0001-7430-2843","observed_orcids":["https://orcid.org/0000-0001-7430-2843"]},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bamdev Mishra","raw_affiliation_strings":["Universit\u00e9 de Li\u00e8ge - ULi\u00e8ge > D\u00e9p. d'\u00e9lectric., \u00e9lectron. et informat. (Inst.Montefiore) > Syst\u00e8mes et mod\u00e9lisation >  >"],"raw_orcid":"https://orcid.org/0000-0001-7430-2843","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Li\u00e8ge - ULi\u00e8ge > D\u00e9p. d'\u00e9lectric., \u00e9lectron. et informat. (Inst.Montefiore) > Syst\u00e8mes et mod\u00e9lisation >  >","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023551959"],"corresponding_institution_ids":["https://openalex.org/I157674565"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9477999806404114,"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":0.9477999806404114,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.020600000396370888,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.007300000172108412,"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/riemannian-optimization","display_name":"Riemannian optimization","score":0.9869999885559082},{"id":"https://openalex.org/keywords/constrained-least-squares","display_name":"constrained least squares","score":0.8880000114440918},{"id":"https://openalex.org/keywords/symmetry-constraints","display_name":"symmetry constraints","score":0.6930000185966492},{"id":"https://openalex.org/keywords/equivalence-relations","display_name":"equivalence relations","score":0.5550000071525574},{"id":"https://openalex.org/keywords/riemannian-metrics","display_name":"Riemannian metrics","score":0.9139999747276306},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"matrix completion","score":0.7770000100135803},{"id":"https://openalex.org/keywords/rank-constraint","display_name":"rank constraint","score":0.9570000171661377},{"id":"https://openalex.org/keywords/generalized-eigenvalue-problem","display_name":"generalized eigenvalue problem","score":0.9959999918937683},{"id":"https://openalex.org/keywords/orthogonality-constraints","display_name":"orthogonality constraints","score":0.9919999837875366},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"sequential quadratic programming","score":0.8790000081062317},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"quadratic programming","score":0.7450000047683716},{"id":"https://openalex.org/keywords/power-iteration","display_name":"power iteration","score":0.765999972820282},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"inverse iteration","score":0.9380000233650208},{"id":"https://openalex.org/keywords/rayleigh-quotient-iteration","display_name":"Rayleigh quotient iteration","score":0.9779999852180481},{"id":"https://openalex.org/keywords/large-scale-optimization","display_name":"large-scale optimization","score":0.9089999794960022}],"concepts":[{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.6066113114356995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4748111963272095},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.4527953863143921},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34769976139068604},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34216874837875366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25044238567352295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20353078842163086},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:orbi.ulg.ac.be:2268/173257","doi":null,"is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/173257","pdf_url":"https://orbi.uliege.be/handle/2268/173257","source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"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":null,"raw_type":"http://purl.org/coar/resource_type/c_db06"},{"id":"mag:81570845","doi":null,"is_oa":false,"landing_page_url":"http://bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-10102014-120708/unrestricted/Oct23_BM_Thesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:orbi.ulg.ac.be:2268/173257","doi":null,"is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/173257","pdf_url":"https://orbi.uliege.be/handle/2268/173257","source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"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":null,"raw_type":"http://purl.org/coar/resource_type/c_db06"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323329","display_name":"Universit\u00e9 de Li\u00e8ge","ror":"https://ror.org/00afp2z80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W81570845.pdf","grobid_xml":"https://content.openalex.org/works/W81570845.grobid-xml"},"referenced_works_count":95,"referenced_works":["https://openalex.org/W128209428","https://openalex.org/W191817552","https://openalex.org/W301566927","https://openalex.org/W1542343170","https://openalex.org/W1546847949","https://openalex.org/W1557324374","https://openalex.org/W1568229137","https://openalex.org/W1573301526","https://openalex.org/W1706213869","https://openalex.org/W1803592988","https://openalex.org/W1804110266","https://openalex.org/W1855068118","https://openalex.org/W1923779967","https://openalex.org/W1964400575","https://openalex.org/W1976618413","https://openalex.org/W1981745143","https://openalex.org/W1983104971","https://openalex.org/W1983482668","https://openalex.org/W1996267928","https://openalex.org/W1996870483","https://openalex.org/W1998367754","https://openalex.org/W2005400753","https://openalex.org/W2011359124","https://openalex.org/W2019781611","https://openalex.org/W2027924293","https://openalex.org/W2037253724","https://openalex.org/W2037562549","https://openalex.org/W2042182457","https://openalex.org/W2043597843","https://openalex.org/W2045123130","https://openalex.org/W2045512849","https://openalex.org/W2047071281","https://openalex.org/W2056405837","https://openalex.org/W2058078260","https://openalex.org/W2060204507","https://openalex.org/W2062388999","https://openalex.org/W2069552222","https://openalex.org/W2078248112","https://openalex.org/W2079354271","https://openalex.org/W2081962379","https://openalex.org/W2086052791","https://openalex.org/W2086953401","https://openalex.org/W2087700323","https://openalex.org/W2088748973","https://openalex.org/W2095984592","https://openalex.org/W2097417531","https://openalex.org/W2097939965","https://openalex.org/W2098670069","https://openalex.org/W2099853640","https://openalex.org/W2101312452","https://openalex.org/W2101593431","https://openalex.org/W2103972604","https://openalex.org/W2105767123","https://openalex.org/W2107654046","https://openalex.org/W2116413942","https://openalex.org/W2116837464","https://openalex.org/W2118550318","https://openalex.org/W2122796095","https://openalex.org/W2126625374","https://openalex.org/W2126762950","https://openalex.org/W2127771846","https://openalex.org/W2131901022","https://openalex.org/W2136289064","https://openalex.org/W2138674039","https://openalex.org/W2143075842","https://openalex.org/W2144112446","https://openalex.org/W2144730813","https://openalex.org/W2145179194","https://openalex.org/W2146130798","https://openalex.org/W2147631863","https://openalex.org/W2150386905","https://openalex.org/W2151211319","https://openalex.org/W2151358751","https://openalex.org/W2151870994","https://openalex.org/W2155779374","https://openalex.org/W2156529323","https://openalex.org/W2158923808","https://openalex.org/W2160634266","https://openalex.org/W2165395308","https://openalex.org/W2167623372","https://openalex.org/W2167758305","https://openalex.org/W2169125102","https://openalex.org/W2169328438","https://openalex.org/W2171151752","https://openalex.org/W2285512060","https://openalex.org/W2296319761","https://openalex.org/W2323887960","https://openalex.org/W2339666411","https://openalex.org/W2520666825","https://openalex.org/W2611328865","https://openalex.org/W2625093932","https://openalex.org/W3037096902","https://openalex.org/W3103022528","https://openalex.org/W3141595720","https://openalex.org/W4253214256"],"related_works":["https://openalex.org/W3037096902","https://openalex.org/W2116837464","https://openalex.org/W1679203207","https://openalex.org/W2058078260","https://openalex.org/W2980860562","https://openalex.org/W7098019363","https://openalex.org/W1996267928","https://openalex.org/W4404341548","https://openalex.org/W2932228020","https://openalex.org/W2167623372"],"abstract_inverted_index":{"This":[0,181],"thesis":[1,251],"deals":[2,252],"with":[3,62,73,222,246,253],"least-squares":[4,25,60,71,102,258],"optimization":[5,111,138,204,220],"on":[6,136,142,162],"a":[7,29,44,59,70,177,194,212],"manifold":[8],"of":[9,16,80,109,121,125,150,157,210],"equivalence":[10],"relations,":[11],"e.g.,":[12],"in":[13,21,93,106,117,214,261],"the":[14,36,48,55,66,86,107,122,143,147,151,155,158,163,207],"presence":[15],"symmetries":[17],"which":[18],"arise":[19],"frequently":[20],"many":[22],"applications.":[23],"While":[24],"cost":[26,159,170],"functions":[27],"remain":[28],"popular":[30],"way":[31,45],"to":[32,46,84,95,167,175],"model":[33],"large-scale":[34,78],"problems,":[35],"additional":[37],"symmetry":[38],"constraint":[39,152],"should":[40],"be":[41],"interpreted":[42],"as":[43,89,91],"make":[47],"modeling":[49],"robust.":[50],"Two":[51],"fundamental":[52,256],"examples":[53],"are":[54,104],"matrix":[56],"completion":[57],"problem,":[58,69],"problem":[61,72,87],"rank":[63,128,225],"constraints":[64,129,172,226],"and":[65,127,171,201,205,224,235,239,259],"generalized":[67],"eigenvalue":[68],"orthogonality":[74,126,223],"constraints.":[75],"The":[76,100],"possible":[77,92],"nature":[79,124],"these":[81],"problems":[82,103,221],"demands":[83],"exploit":[85],"structure":[88],"much":[90,115],"order":[94],"design":[96],"numerically":[97],"efficient":[98],"algorithms.":[99,248],"constrained":[101],"tackled":[105],"framework":[108],"Riemannian":[110,137,179,187,202,215],"that":[112,130,243],"has":[113,139],"gained":[114],"popularity":[116],"recent":[118],"years":[119],"because":[120],"special":[123],"have":[131],"particular":[132],"symmetries.":[133],"Previous":[134],"work":[135],"mostly":[140],"focused":[141],"search":[144],"space,":[145],"exploiting":[146,254],"differential":[148],"geometry":[149],"but":[153],"disregarding":[154],"role":[156],"function.":[160],"We,":[161],"other":[164],"hand,":[165],"propose":[166,176],"take":[168],"both":[169],"into":[173],"account":[174],"tailored":[178],"geometry.":[180],"is":[182],"achieved":[183],"by":[184,227],"proposing":[185,240],"novel":[186,241],"metrics.":[188],"To":[189],"this":[190,250],"end,":[191],"we":[192],"show":[193],"basic":[195],"connection":[196],"between":[197],"sequential":[198],"quadratic":[199,219],"programming":[200],"gradient":[203],"address":[206],"general":[208],"question":[209],"selecting":[211],"metric":[213],"optimization.":[216,263],"We":[217],"revisit":[218],"generalizing":[228],"various":[229],"existing":[230],"methods,":[231],"like":[232],"power,":[233],"inverse":[234],"Rayleigh":[236],"quotient":[237],"iterations,":[238],"ones":[242],"empirically":[244],"compete":[245],"state-of-the-art":[247],"Overall,":[249],"two":[255],"structures,":[257],"symmetry,":[260],"nonlinear":[262]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}