{"id":"https://openalex.org/W2140881476","doi":"https://doi.org/10.1137/130917661","title":"A Merit Function Approach for Direct Search","display_name":"A Merit Function Approach for Direct Search","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2140881476","doi":"https://doi.org/10.1137/130917661","mag":"2140881476"},"language":"en","primary_location":{"id":"doi:10.1137/130917661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130917661","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":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036298459","display_name":"Serge Gratton","orcid":"https://orcid.org/0000-0002-5021-2357"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Gratton","raw_affiliation_strings":["IRIT - Institut de recherche en informatique de Toulouse (118 Route de Narbonne, F-31062 Toulouse Cedex 9 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT - Institut de recherche en informatique de Toulouse (118 Route de Narbonne, F-31062 Toulouse Cedex 9 - France)","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045737795","display_name":"L. N. Vicente","orcid":"https://orcid.org/0000-0003-1097-6384"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. N. Vicente","raw_affiliation_strings":["CMUC - Center for Mathematics [Coimbra] (Department of Mathematics - Apartado 3008, EC Santa Cruz, 3001-501 Coimbra - Portugal)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMUC - Center for Mathematics [Coimbra] (Department of Mathematics - Apartado 3008, EC Santa Cruz, 3001-501 Coimbra - Portugal)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2337,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.91547278,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"4","first_page":"1980","last_page":"1998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.994700014591217,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6994503140449524},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6279255747795105},{"id":"https://openalex.org/keywords/figure-of-merit","display_name":"Figure of merit","score":0.5596284866333008},{"id":"https://openalex.org/keywords/novelty","display_name":"Novelty","score":0.5511002540588379},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.548554003238678},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.512290358543396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48626625537872314},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4808664917945862},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4178425073623657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38709917664527893}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6994503140449524},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6279255747795105},{"id":"https://openalex.org/C130277099","wikidata":"https://www.wikidata.org/wiki/Q3676605","display_name":"Figure of merit","level":2,"score":0.5596284866333008},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.5511002540588379},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.548554003238678},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.512290358543396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48626625537872314},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4808664917945862},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4178425073623657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38709917664527893},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"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/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/130917661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130917661","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:oatao.univ-toulouse.fr:22599","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.417.7555","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.417.7555","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mat.uc.pt/~lnv/papers/merit.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.432.4157","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.432.4157","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mat.uc.pt/~lnv/papers/merit.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03519555v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03519555","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2014, 24 (4), pp.1980-1998. &#x27E8;10.1137/130917661&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:estudogeral.sib.uc.pt:10316/45560","is_oa":false,"landing_page_url":"http://hdl.handle.net/10316/45560","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"pmh:oai:oatao.univ-toulouse.fr:22599","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W164858012","https://openalex.org/W181733065","https://openalex.org/W1451881698","https://openalex.org/W1551360398","https://openalex.org/W1552227532","https://openalex.org/W1780196089","https://openalex.org/W1977630551","https://openalex.org/W1994895518","https://openalex.org/W1998855065","https://openalex.org/W2005337722","https://openalex.org/W2006575733","https://openalex.org/W2014337138","https://openalex.org/W2019362739","https://openalex.org/W2021940557","https://openalex.org/W2024948279","https://openalex.org/W2064215934","https://openalex.org/W2071436527","https://openalex.org/W2077594413","https://openalex.org/W2079854116","https://openalex.org/W2084186221","https://openalex.org/W2133356919","https://openalex.org/W2142960723","https://openalex.org/W2148563791","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W2381242807","https://openalex.org/W3126131230","https://openalex.org/W2347541121","https://openalex.org/W4288804799","https://openalex.org/W2080951048","https://openalex.org/W3032237421","https://openalex.org/W2390346111","https://openalex.org/W3011883280","https://openalex.org/W2369082698","https://openalex.org/W2401808953"],"abstract_inverted_index":{"In":[0],"this":[1,55],"paper":[2],"it":[3],"is":[4,106],"proposed":[5],"to":[6,14,26,108,149,159],"equip":[7],"direct-search":[8,115],"methods":[9],"with":[10],"a":[11,82,89,147],"general":[12],"procedure":[13],"minimize":[15],"an":[16,101],"objective":[17],"function,":[18],"possibly":[19],"nonsmooth,":[20,40],"without":[21],"using":[22],"derivatives":[23,44],"and":[24,133],"subject":[25],"constraints":[27,62,154],"on":[28,59],"the":[29,43,46,72,75,111,127,151,156,160],"variables.":[30],"One":[31,105],"aims":[32],"at":[33],"considering":[34],"constraints,":[35,66],"most":[36],"likely":[37],"nonlinear":[38],"or":[39],"for":[41,121],"which":[42,67],"of":[45,54,74,80,153],"corresponding":[47],"functions":[48],"are":[49,63,77,94,98],"also":[50],"unavailable.":[51],"The":[52],"novelty":[53],"contribution":[56],"relies":[57],"mostly":[58],"how":[60],"relaxable":[61,157],"handled.":[64],"Such":[65],"can":[68],"be":[69],"relaxed":[70],"during":[71],"course":[73],"optimization,":[76],"taken":[78],"care":[79],"by":[81,88,100],"merit":[83,113],"function":[84,114],"and,":[85],"if":[86],"necessary,":[87],"restoration":[90],"procedure.":[91],"Constraints":[92],"that":[93,110],"unrelaxable,":[95],"when":[96],"present,":[97],"treated":[99],"extreme":[102],"barrier":[103,129],"approach.":[104],"able":[107],"show":[109],"resulting":[112],"algorithm":[116],"exhibits":[117],"global":[118],"convergence":[119],"properties":[120],"first-order":[122],"stationary":[123],"constraints.":[124],"As":[125],"in":[126],"progressive":[128],"method":[130],"[C.":[131],"Audet":[132],"J.":[134,139],"E.":[135],"Dennis":[136],"Jr.,":[137],"SIAM":[138],"Optim.,":[140],"20":[141],"(2009),":[142],"pp.":[143],"445--472],":[144],"we":[145],"provide":[146],"mechanism":[148],"indicate":[150],"transfer":[152],"from":[155],"set":[158],"unrelaxable":[161],"one.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
