{"id":"https://openalex.org/W1998855065","doi":"https://doi.org/10.1137/040603371","title":"Mesh Adaptive Direct Search Algorithms for Constrained Optimization","display_name":"Mesh Adaptive Direct Search Algorithms for Constrained Optimization","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1998855065","doi":"https://doi.org/10.1137/040603371","mag":"1998855065"},"language":"en","primary_location":{"id":"doi:10.1137/040603371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603371","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5089929904","display_name":"Charles Audet","orcid":"https://orcid.org/0000-0002-3043-5393"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Charles Audet","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109961247","display_name":"J. E. Dennis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. E. Dennis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089929904"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":44.3515,"has_fulltext":false,"cited_by_count":1206,"citation_normalized_percentile":{"value":0.99975069,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"17","issue":"1","first_page":"188","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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":0.9987000226974487,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9980999827384949,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.7197132706642151},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5508357882499695},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4857175946235657},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.46465176343917847},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4363236725330353},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43526801466941833},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39268407225608826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23948723077774048}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7197132706642151},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5508357882499695},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4857175946235657},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.46465176343917847},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4363236725330353},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43526801466941833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39268407225608826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23948723077774048},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040603371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603371","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:publications.polymtl.ca:22290","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/22290/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W32104792","https://openalex.org/W62429925","https://openalex.org/W125310434","https://openalex.org/W1487974501","https://openalex.org/W1493249195","https://openalex.org/W1551360398","https://openalex.org/W1552227532","https://openalex.org/W1590012787","https://openalex.org/W1971200627","https://openalex.org/W1973518536","https://openalex.org/W1976168680","https://openalex.org/W1979881015","https://openalex.org/W1985412770","https://openalex.org/W2005874105","https://openalex.org/W2006575733","https://openalex.org/W2014337138","https://openalex.org/W2019362739","https://openalex.org/W2038669746","https://openalex.org/W2054875385","https://openalex.org/W2056621397","https://openalex.org/W2061368966","https://openalex.org/W2062988270","https://openalex.org/W2070922270","https://openalex.org/W2079854116","https://openalex.org/W2084186221","https://openalex.org/W2097273628","https://openalex.org/W2162737890","https://openalex.org/W2312715465","https://openalex.org/W4212993107","https://openalex.org/W4237209688","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W3103325625","https://openalex.org/W1486898455","https://openalex.org/W3090727460","https://openalex.org/W2041905724","https://openalex.org/W2047986527","https://openalex.org/W4306313719","https://openalex.org/W3128682647","https://openalex.org/W2991463004","https://openalex.org/W1983011418","https://openalex.org/W1976246538"],"abstract_inverted_index":{"This":[0,64],"paper":[1,174],"addresses":[2],"the":[3,19,28,39,59,83,89,98,114,131,140,143,159,177,186,198,211,217,226,230,255,271,274],"problem":[4,99],"of":[5,7,18,35,56,61,87,124,136,158,172,188,193,207,240,246,257,273],"minimization":[6],"a":[8,71,121,235],"nonsmooth":[9,13],"function":[10],"under":[11,67],"general":[12,178],"constraints":[14,81,166],"when":[15],"no":[16],"derivatives":[17,117,200],"objective":[20,90],"or":[21],"constraint":[22,73],"functions":[23],"are":[24,118,201,214],"available.":[25],"We":[26,203,252],"introduce":[27],"mesh":[29],"adaptive":[30],"direct":[31],"search":[32,42],"(MADS)":[33],"class":[34,44],"algorithms":[36],"which":[37,197,210],"extends":[38],"generalized":[40,116],"pattern":[41],"(GPS)":[43],"by":[45,82],"allowing":[46],"local":[47],"exploration,":[48],"called":[49,126],"polling,":[50],"in":[51,58,120,130,216],"an":[52,189,205],"asymptotically":[53,190],"dense":[54,191,215],"set":[55,123,192],"directions":[57,138,154,195,213,232],"space":[60],"optimization":[62],"variables.":[63],"means":[65],"that":[66,145,176],"certain":[68],"hypotheses,":[69],"including":[70],"weak":[72],"qualification":[74],"due":[75],"to":[76,91,108,162,184,234,244,264],"Rockafellar,":[77],"MADS":[78,179,208,241],"can":[79,147],"treat":[80],"extreme":[84],"barrier":[85,160],"approach":[86,161],"setting":[88],"infinity":[92],"for":[93,167,209],"infeasible":[94],"points":[95,111],"and":[96],"treating":[97],"as":[100],"unconstrained.":[101],"The":[102,169,238],"main":[103,170],"GPS":[104,152,247],"convergence":[105],"result":[106,171],"is":[107,175,181,242],"identify":[109],"limit":[110],"$\\hat{x}$,":[112],"where":[113],"Clarke":[115,199],"nonnegative":[119,134],"finite":[122],"directions,":[125],"refining":[127,153,194,212,231],"directions.":[128],"Although":[129],"unconstrained":[132],"case,":[133],"combinations":[135],"these":[137],"span":[139],"whole":[141],"space,":[142],"fact":[144],"there":[146],"only":[148],"be":[149],"finitely":[150,163],"many":[151,164],"limits":[155],"rigorous":[156],"justification":[157],"linear":[165],"GPS.":[168],"this":[173,265],"framework":[180],"flexible":[182],"enough":[183],"allow":[185],"generation":[187],"along":[196],"nonnegative.":[202],"propose":[204],"instance":[206,239],"hypertangent":[218],"cone":[219],"at":[220,270],"$\\hat{x}$":[221],"with":[222,229,260],"probability":[223],"1":[224],"whenever":[225],"iterates":[227],"associated":[228],"converge":[233],"single":[236],"$\\hat{x}$.":[237],"compared":[243],"versions":[245],"on":[248],"some":[249],"test":[250],"problems.":[251],"also":[253],"illustrate":[254],"limitation":[256],"our":[258],"results":[259],"examples.":[261],"An":[262],"erratum":[263],"article":[266],"has":[267],"been":[268],"appended":[269],"end":[272],"pdf":[275],"file.":[276]},"counts_by_year":[{"year":2026,"cited_by_count":20},{"year":2025,"cited_by_count":55},{"year":2024,"cited_by_count":58},{"year":2023,"cited_by_count":58},{"year":2022,"cited_by_count":72},{"year":2021,"cited_by_count":100},{"year":2020,"cited_by_count":89},{"year":2019,"cited_by_count":76},{"year":2018,"cited_by_count":73},{"year":2017,"cited_by_count":81},{"year":2016,"cited_by_count":62},{"year":2015,"cited_by_count":62},{"year":2014,"cited_by_count":80},{"year":2013,"cited_by_count":66},{"year":2012,"cited_by_count":47}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}