{"id":"https://openalex.org/W2006984156","doi":"https://doi.org/10.1109/jsac.1986.1146414","title":"On Lagrange Multipliers in Work with Quality and Reliability Assurance","display_name":"On Lagrange Multipliers in Work with Quality and Reliability Assurance","publication_year":1986,"publication_date":"1986-10-01","ids":{"openalex":"https://openalex.org/W2006984156","doi":"https://doi.org/10.1109/jsac.1986.1146414","mag":"2006984156"},"language":"en","primary_location":{"id":"doi:10.1109/jsac.1986.1146414","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.1986.1146414","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Journal on Selected Areas in Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbit.dtu.dk/en/publications/bbb46620-3feb-441e-9525-5290e32f57ca","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112302328","display_name":"Ren\u00e9 V\u00edctor Valqui Vidal","orcid":null},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"R. Vidal","raw_affiliation_strings":["Technical University of Denmark, Lyngby, Denmark","Tech. Univ. of Denmark, Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Tech. Univ. of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103003876","display_name":"Peter W. Becker","orcid":"https://orcid.org/0000-0002-9649-4839"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"P. Becker","raw_affiliation_strings":["Technical University of Denmark, Lyngby, Denmark","Technical University of Denmark,,,Lyngby,,Denmark"],"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Technical University of Denmark,,,Lyngby,,Denmark","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112302328"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.13200498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"7","first_page":"1143","last_page":"1148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9897000193595886,"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":0.9897000193595886,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9688000082969666,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9674999713897705,"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/computer-science","display_name":"Computer science","score":0.7941749095916748},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7773987054824829},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6753348112106323},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5873535871505737},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5400837659835815},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5174944400787354},{"id":"https://openalex.org/keywords/quality","display_name":"Quality (philosophy)","score":0.42719486355781555},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3446086347103119},{"id":"https://openalex.org/keywords/reliability-engineering","display_name":"Reliability engineering","score":0.3306269645690918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13891005516052246}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7941749095916748},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7773987054824829},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6753348112106323},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5873535871505737},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5400837659835815},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5174944400787354},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.42719486355781555},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3446086347103119},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.3306269645690918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13891005516052246},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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":2,"locations":[{"id":"doi:10.1109/jsac.1986.1146414","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.1986.1146414","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Journal on Selected Areas in Communications","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/bbb46620-3feb-441e-9525-5290e32f57ca","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/bbb46620-3feb-441e-9525-5290e32f57ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"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":"Vidal , R V V & Becker , P 1986 , ' On Lagrange Multipliers in Work with Quality and Reliability Assurance ' , I E E E Journal on Selected Areas in Communications , vol. 4 , no. 7 , pp. 1143-1148 . https://doi.org/10.1109/JSAC.1986.1146414","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/bbb46620-3feb-441e-9525-5290e32f57ca","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/bbb46620-3feb-441e-9525-5290e32f57ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"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":"Vidal , R V V & Becker , P 1986 , ' On Lagrange Multipliers in Work with Quality and Reliability Assurance ' , I E E E Journal on Selected Areas in Communications , vol. 4 , no. 7 , pp. 1143-1148 . https://doi.org/10.1109/JSAC.1986.1146414","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1520763683","https://openalex.org/W1976177052","https://openalex.org/W1982076739","https://openalex.org/W1987812542","https://openalex.org/W2021118809","https://openalex.org/W2035747964","https://openalex.org/W2062282137","https://openalex.org/W2069277547","https://openalex.org/W2145388448","https://openalex.org/W3011744285","https://openalex.org/W3143914623","https://openalex.org/W6775133946"],"related_works":["https://openalex.org/W2033512842","https://openalex.org/W4322734194","https://openalex.org/W1607054433","https://openalex.org/W3005535424","https://openalex.org/W4233600955","https://openalex.org/W2913665393","https://openalex.org/W2994319598","https://openalex.org/W2369695847","https://openalex.org/W2110842462","https://openalex.org/W4233757488"],"abstract_inverted_index":{"In":[0],"optimizing":[1],"some":[2],"property":[3],"of":[4,26,39,47,53,79,90,101,112,116],"a":[5,9],"system,":[6],"reliability":[7],"say,":[8],"designer":[10],"usually":[11],"has":[12],"to":[13,67,84],"accept":[14],"certain":[15],"constraints":[16,31],"regarding":[17],"cost,":[18],"completion":[19],"time,":[20],"volume,":[21],"weight,":[22],"etc.":[23],"The":[24],"solution":[25,102],"optimization":[27],"problems":[28],"with":[29],"boundary":[30],"can":[32],"be":[33,85],"helped":[34],"substantially":[35],"by":[36],"the":[37,50,77,88,98,110,117],"use":[38],"Lagrange":[40],"multipliers":[41],"techniques":[42],"(LMT).":[43],"With":[44],"representative":[45],"examples":[46],"increasing":[48],"complexity,":[49],"wide":[51],"applicability":[52],"LMT":[54,113],"is":[55,74,82,107],"illustrated.":[56],"Two":[57],"particular":[58],"features":[59],"are":[60],"put":[61],"in":[62,87,114],"focus.":[63],"First,":[64],"an":[65],"easy":[66],"follow":[68],"yet":[69],"powerful":[70],"new":[71],"graphical":[72],"approach":[73],"presented,":[75],"Second,":[76],"concept":[78],"Fuller-Polya":[80],"maps":[81,96],"shown":[83],"helpful":[86],"areas":[89],"sales":[91],"promotion":[92],"and":[93],"teaching.":[94],"These":[95],"illuminate":[97],"logic":[99],"structure":[100],"sequences.":[103],"One":[104],"such":[105],"map":[106],"shown,":[108],"illustrating":[109],"application":[111],"one":[115],"examples.":[118]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}