{"id":"https://openalex.org/W4405185950","doi":"https://doi.org/10.3390/a17120563","title":"Issues on a 2\u2013Dimensional Quadratic Sub\u2013Problem and Its Applications in Nonlinear Programming: Trust\u2013Region Methods (TRMs) and Linesearch Based Methods (LBMs)","display_name":"Issues on a 2\u2013Dimensional Quadratic Sub\u2013Problem and Its Applications in Nonlinear Programming: Trust\u2013Region Methods (TRMs) and Linesearch Based Methods (LBMs)","publication_year":2024,"publication_date":"2024-12-09","ids":{"openalex":"https://openalex.org/W4405185950","doi":"https://doi.org/10.3390/a17120563"},"language":"en","primary_location":{"id":"doi:10.3390/a17120563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17120563","pdf_url":"https://www.mdpi.com/1999-4893/17/12/563/pdf?version=1733739452","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/17/12/563/pdf?version=1733739452","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008549672","display_name":"Giovanni Fasano","orcid":"https://orcid.org/0000-0003-4721-8114"},"institutions":[{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giovanni Fasano","raw_affiliation_strings":["Department of Management, Venice School of Management, Ca\u2019 Foscari University, S. Giobbe, Cannaregio 873, 30121 Venice, Italy","Department of Management, Venice School of Management, Ca' Foscari University, S. Giobbe, Cannaregio 873, 30121 Venice, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4721-8114","affiliations":[{"raw_affiliation_string":"Department of Management, Venice School of Management, Ca\u2019 Foscari University, S. Giobbe, Cannaregio 873, 30121 Venice, Italy","institution_ids":["https://openalex.org/I149461666"]},{"raw_affiliation_string":"Department of Management, Venice School of Management, Ca' Foscari University, S. Giobbe, Cannaregio 873, 30121 Venice, Italy","institution_ids":["https://openalex.org/I149461666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090232559","display_name":"Christian Piermarini","orcid":null},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Christian Piermarini","raw_affiliation_strings":["Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042713763","display_name":"Massimo Roma","orcid":"https://orcid.org/0000-0002-9858-3616"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimo Roma","raw_affiliation_strings":["Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9858-3616","affiliations":[{"raw_affiliation_string":"Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008549672"],"corresponding_institution_ids":["https://openalex.org/I149461666"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29061284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"12","first_page":"563","last_page":"563"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9948999881744385,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944000244140625,"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.9313596487045288},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.7498260736465454},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.678433895111084},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.605918824672699},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5574246644973755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49877262115478516},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.49870729446411133},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49386268854141235},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.4692898690700531},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.451337605714798},{"id":"https://openalex.org/keywords/analogy","display_name":"Analogy","score":0.42874929308891296},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4005098342895508},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07549852132797241},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05179470777511597}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9313596487045288},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.7498260736465454},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.678433895111084},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.605918824672699},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5574246644973755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49877262115478516},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.49870729446411133},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49386268854141235},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.4692898690700531},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.451337605714798},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.42874929308891296},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4005098342895508},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07549852132797241},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05179470777511597},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","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":4,"locations":[{"id":"doi:10.3390/a17120563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17120563","pdf_url":"https://www.mdpi.com/1999-4893/17/12/563/pdf?version=1733739452","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:iris.unive.it:10278/5084998","is_oa":true,"landing_page_url":"https://www.mdpi.com/1999-4893/17/12/563","pdf_url":"https://iris.unive.it/bitstream/10278/5084998/1/algorithms-17-00563.pdf","source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:3d1a6945ddd049c0a991b27554bae3f4","is_oa":false,"landing_page_url":"https://doaj.org/article/3d1a6945ddd049c0a991b27554bae3f4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Algorithms, Vol 17, Iss 12, p 563 (2024)","raw_type":"article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1729323","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1729323","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/a17120563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17120563","pdf_url":"https://www.mdpi.com/1999-4893/17/12/563/pdf?version=1733739452","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405185950.pdf","grobid_xml":"https://content.openalex.org/works/W4405185950.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W603729728","https://openalex.org/W1568307856","https://openalex.org/W1580352598","https://openalex.org/W1969849531","https://openalex.org/W1984488466","https://openalex.org/W1990689599","https://openalex.org/W1993650230","https://openalex.org/W1997965167","https://openalex.org/W2000389939","https://openalex.org/W2022090011","https://openalex.org/W2035072927","https://openalex.org/W2039676703","https://openalex.org/W2045676435","https://openalex.org/W2058731384","https://openalex.org/W2063690908","https://openalex.org/W2107501462","https://openalex.org/W2118700449","https://openalex.org/W2487584502","https://openalex.org/W2766556641","https://openalex.org/W2767098649","https://openalex.org/W2963321060","https://openalex.org/W3046263807","https://openalex.org/W4244829582","https://openalex.org/W4386328668"],"related_works":["https://openalex.org/W1555927645","https://openalex.org/W1548320777","https://openalex.org/W4206704743","https://openalex.org/W2119283772","https://openalex.org/W2019128690","https://openalex.org/W436931041","https://openalex.org/W2098918699","https://openalex.org/W1495847109","https://openalex.org/W2390817143","https://openalex.org/W2106813160"],"abstract_inverted_index":{"This":[0],"paper":[1],"analyses":[2],"the":[3,50],"solution":[4,51,80],"of":[5,34,52,81],"a":[6,32,46,59],"specific":[7],"quadratic":[8,62,84],"sub-problem,":[9,85],"along":[10],"with":[11,49],"its":[12],"possible":[13],"applications,":[14],"within":[15],"both":[16],"constrained":[17],"and":[18,40],"unconstrained":[19],"Nonlinear":[20],"Programming":[21],"frameworks.":[22],"We":[23],"give":[24],"evidence":[25],"that":[26],"this":[27],"sub\u2013problem":[28],"may":[29],"appear":[30],"in":[31],"number":[33],"Linesearch":[35],"Based":[36],"Methods":[37],"(LBM)":[38],"schemes,":[39],"to":[41,58,75],"some":[42],"extent":[43],"it":[44],"reveals":[45],"close":[47],"analogy":[48],"trust\u2013region":[53],"sub\u2013problems.":[54],"Namely,":[55],"we":[56,72],"refer":[57],"two-dimensional":[60,83],"structured":[61],"problem,":[63],"where":[64],"five":[65],"linear":[66],"inequality":[67],"constraints":[68],"are":[69],"included.":[70],"Finally,":[71],"detail":[73],"how":[74],"compute":[76],"an":[77],"exact":[78],"global":[79],"our":[82],"exploiting":[86],"first":[87],"order":[88],"Karush-Khun-Tucker":[89],"(KKT)":[90],"conditions.":[91]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}