{"id":"https://openalex.org/W2337830179","doi":"https://doi.org/10.1080/10556788.2015.1135919","title":"Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints","display_name":"Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints","publication_year":2016,"publication_date":"2016-02-05","ids":{"openalex":"https://openalex.org/W2337830179","doi":"https://doi.org/10.1080/10556788.2015.1135919","mag":"2337830179"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2015.1135919","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1135919","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5041442159","display_name":"Ph. R. Sampaio","orcid":null},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Ph. R. Sampaio","raw_affiliation_strings":["Namur Center for Complex Systems (naXys) and Department of Mathematics, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium"],"affiliations":[{"raw_affiliation_string":"Namur Center for Complex Systems (naXys) and Department of Mathematics, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002913605","display_name":"Philippe L. Toint","orcid":"https://orcid.org/0000-0002-6166-1860"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Ph. L. Toint","raw_affiliation_strings":["Namur Center for Complex Systems (naXys) and Department of Mathematics, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium"],"affiliations":[{"raw_affiliation_string":"Namur Center for Complex Systems (naXys) and Department of Mathematics, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041442159"],"corresponding_institution_ids":["https://openalex.org/I149768937"],"apc_list":null,"apc_paid":null,"fwci":1.825,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8331945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"3","first_page":"511","last_page":"534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9861999750137329,"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":0.9850999712944031,"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/funnel","display_name":"Funnel","score":0.9061346054077148},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6557568311691284},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6524996757507324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6447018980979919},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.6308683753013611},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.6308273077011108},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6121224164962769},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5139297842979431},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49940943717956543},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4776519536972046},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.45333629846572876},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.4434354305267334},{"id":"https://openalex.org/keywords/derivative-free-optimization","display_name":"Derivative-free optimization","score":0.43047139048576355},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41901472210884094},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.4115699529647827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2711780071258545},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07431384921073914}],"concepts":[{"id":"https://openalex.org/C17435862","wikidata":"https://www.wikidata.org/wiki/Q29957","display_name":"Funnel","level":2,"score":0.9061346054077148},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6557568311691284},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6524996757507324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6447018980979919},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6308683753013611},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.6308273077011108},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6121224164962769},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5139297842979431},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49940943717956543},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4776519536972046},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.45333629846572876},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.4434354305267334},{"id":"https://openalex.org/C29282572","wikidata":"https://www.wikidata.org/wiki/Q16977029","display_name":"Derivative-free optimization","level":4,"score":0.43047139048576355},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41901472210884094},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.4115699529647827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2711780071258545},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07431384921073914},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2015.1135919","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1135919","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W181733065","https://openalex.org/W1451881698","https://openalex.org/W1748199557","https://openalex.org/W1973734200","https://openalex.org/W1982087768","https://openalex.org/W2006575733","https://openalex.org/W2013261078","https://openalex.org/W2019362739","https://openalex.org/W2057565823","https://openalex.org/W2057830724","https://openalex.org/W2079777091","https://openalex.org/W2084186221","https://openalex.org/W2088118089","https://openalex.org/W2093483979","https://openalex.org/W2095691822","https://openalex.org/W2108957175","https://openalex.org/W2132492300","https://openalex.org/W2143447201","https://openalex.org/W2149454052","https://openalex.org/W2333358170","https://openalex.org/W4252626574"],"related_works":["https://openalex.org/W2912146214","https://openalex.org/W4312509357","https://openalex.org/W2936968591","https://openalex.org/W1536944467","https://openalex.org/W3092127437","https://openalex.org/W2596893084","https://openalex.org/W2386439376","https://openalex.org/W2063398976","https://openalex.org/W2183030025","https://openalex.org/W2083103858"],"abstract_inverted_index":{"A":[0],"trust-funnel":[1,140,155],"method":[2,63,105,141,156],"is":[3,91],"proposed":[4,37],"for":[5,38,98,142,157,177],"solving":[6],"nonlinear":[7,12,144],"optimization":[8,40,100],"problems":[9,41,44,113],"with":[10,45,162],"general":[11],"constraints.":[13],"It":[14],"extends":[15,129],"the":[16,59,74,78,86,115,130,163],"one":[17],"presented":[18,133],"by":[19,134],"Gould":[20],"and":[21,48,51,72,77,136],"Toint":[22,137],"[Nonlinear":[23],"programming":[24],"without":[25],"a":[26,30,104,123,153],"penalty":[27,70],"function":[28,76],"or":[29,119],"filter.":[31],"Math.":[32],"Prog.":[33],"122(1):155\u2013196,":[34],"2010],":[35],"originally":[36],"equality-constrained":[39,143,158],"only,":[42],"to":[43,102,111,172],"both":[46],"equality":[47],"inequality":[49],"constraints":[50,79],"where":[52,114],"simple":[53],"bounds":[54],"are":[55,117,120],"also":[56,108],"considered.":[57],"As":[58],"original":[60],"one,":[61],"our":[62,168],"makes":[64],"use":[65],"of":[66],"neither":[67],"filter":[68],"nor":[69],"functions":[71],"considers":[73],"objective":[75],"as":[80,82],"independently":[81],"possible.":[83],"To":[84],"handle":[85],"bounds,":[87],"an":[88],"active-set":[89],"approach":[90,128,169],"employed.":[92],"We":[93],"then":[94],"exploit":[95],"techniques":[96],"developed":[97],"derivative-free":[99,139,154],"(DFO)":[101],"obtain":[103],"that":[106,167],"can":[107],"be":[109],"used":[110],"solve":[112],"derivatives":[116],"unavailable":[118],"available":[121],"at":[122],"prohibitive":[124],"cost.":[125],"The":[126],"resulting":[127],"DEFT-FUNNEL":[131],"algorithm":[132,165],"Sampaio":[135],"[A":[138],"optimization.":[145],"Comput.":[146],"Optim.":[147],"Appl.":[148],"61(1):25\u201349,":[149],"2015],":[150],"which":[151],"implements":[152],"problems.":[159],"Numerical":[160],"experiments":[161],"extended":[164],"show":[166],"compares":[170],"favourably":[171],"other":[173],"well-known":[174],"model-based":[175],"algorithms":[176],"DFO.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}