{"id":"https://openalex.org/W4411558078","doi":"https://doi.org/10.3390/a18070381","title":"Hestenes\u2013Stiefel-Type Conjugate Direction Algorithm for Interval-Valued Multiobjective Optimization Problems","display_name":"Hestenes\u2013Stiefel-Type Conjugate Direction Algorithm for Interval-Valued Multiobjective Optimization Problems","publication_year":2025,"publication_date":"2025-06-23","ids":{"openalex":"https://openalex.org/W4411558078","doi":"https://doi.org/10.3390/a18070381"},"language":"en","primary_location":{"id":"doi:10.3390/a18070381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070381","pdf_url":null,"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://doi.org/10.3390/a18070381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101245269","display_name":"Rupesh K. Pandey","orcid":null},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Rupesh Krishna Pandey","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012427085","display_name":"Balendu Bhooshan Upadhyay","orcid":"https://orcid.org/0000-0002-7115-693X"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Balendu Bhooshan Upadhyay","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5095763912","display_name":"Subham Poddar","orcid":null},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Subham Poddar","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108232657","display_name":"Ioan Stancu-Minasian","orcid":null},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ioan Stancu-Minasian","raw_affiliation_strings":["\u201cGheorghe Mihoc-Caius Iacob\u201d Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"\u201cGheorghe Mihoc-Caius Iacob\u201d Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101245269"],"corresponding_institution_ids":["https://openalex.org/I132153292"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.26,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.94404719,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"18","issue":"7","first_page":"381","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9732999801635742,"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"}},"topics":[{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9732999801635742,"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6846870183944702},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6252986788749695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6120891571044922},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.589095950126648},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5714013576507568},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4947595000267029},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4277610778808594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38292962312698364},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36206650733947754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32310014963150024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2722935676574707},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23343953490257263},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1899339258670807}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6846870183944702},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6252986788749695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6120891571044922},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.589095950126648},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5714013576507568},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4947595000267029},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4277610778808594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38292962312698364},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36206650733947754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32310014963150024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2722935676574707},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23343953490257263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1899339258670807},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a18070381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070381","pdf_url":null,"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:doaj.org/article:5d39ec87417b4939ab4e9a267f8dddb8","is_oa":true,"landing_page_url":"https://doaj.org/article/5d39ec87417b4939ab4e9a267f8dddb8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 7, p 381 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18070381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070381","pdf_url":null,"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":[],"awards":[{"id":"https://openalex.org/G5642764258","display_name":null,"funder_award_id":"PMRF ID-2703573","funder_id":"https://openalex.org/F4320322724","funder_display_name":"Ministry of Education, India"}],"funders":[{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1580809199","https://openalex.org/W1994833677","https://openalex.org/W2001359285","https://openalex.org/W2008499862","https://openalex.org/W2009054772","https://openalex.org/W2018332842","https://openalex.org/W2029840249","https://openalex.org/W2034038007","https://openalex.org/W2044778367","https://openalex.org/W2057578284","https://openalex.org/W2073833672","https://openalex.org/W2088735768","https://openalex.org/W2100717205","https://openalex.org/W2108560279","https://openalex.org/W2316564661","https://openalex.org/W2751964841","https://openalex.org/W2801266866","https://openalex.org/W2893010165","https://openalex.org/W2986483861","https://openalex.org/W3022544804","https://openalex.org/W3106370860","https://openalex.org/W3173451412","https://openalex.org/W3215710774","https://openalex.org/W4206824823","https://openalex.org/W4225873238","https://openalex.org/W4237728623","https://openalex.org/W4293775970","https://openalex.org/W4310154744","https://openalex.org/W4381331453","https://openalex.org/W4386800052","https://openalex.org/W4387756559","https://openalex.org/W4400237324","https://openalex.org/W4402425807","https://openalex.org/W4403102724","https://openalex.org/W4403839888","https://openalex.org/W4406070662","https://openalex.org/W4408300761","https://openalex.org/W6676921057","https://openalex.org/W6854638055"],"related_works":["https://openalex.org/W2143004018","https://openalex.org/W2330362314","https://openalex.org/W2435669318","https://openalex.org/W1995639836","https://openalex.org/W2103568534","https://openalex.org/W2057862416","https://openalex.org/W2754988198","https://openalex.org/W1543576583","https://openalex.org/W2290850064","https://openalex.org/W1503783781"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"a":[3,28,73,102],"class":[4,137],"of":[5,21,59,76,87,109,122,138],"interval-valued":[6],"multiobjective":[7],"optimization":[8],"problems":[9],"(IVMOPs).":[10],"We":[11,46,66],"define":[12],"the":[13,18,57,60,64,69,84,88,92,107,120,125,136],"Hestenes\u2013Stiefel":[14],"(HS)-type":[15],"direction":[16,51,128],"for":[17,53,135],"objective":[19],"function":[20],"IVMOPs":[22,54],"and":[23,55,113],"establish":[24,56],"that":[25,68],"it":[26],"has":[27,130],"descent":[29],"property":[30],"at":[31],"noncritical":[32],"points.":[33],"An":[34],"Armijo-like":[35],"line":[36],"search":[37],"is":[38],"employed":[39],"to":[40,105],"determine":[41],"an":[42,48],"appropriate":[43,79],"step":[44],"size.":[45],"present":[47],"HS-type":[49,126],"conjugate":[50,127],"algorithm":[52,71,112],"convergence":[58,77],"sequence":[61,89],"generated":[62,90],"by":[63,91,116],"algorithm.":[65,94],"deduce":[67],"proposed":[70,93,111],"exhibits":[72],"linear":[74],"order":[75],"under":[78],"assumptions.":[80],"Moreover,":[81],"we":[82,96],"investigate":[83],"worst-case":[85],"complexity":[86],"Furthermore,":[95],"furnish":[97],"several":[98],"numerical":[99],"examples,":[100],"including":[101],"large-scale":[103],"IVMOP,":[104],"demonstrate":[106],"effectiveness":[108],"our":[110,123],"solve":[114],"them":[115],"employing":[117],"MATLAB.":[118],"To":[119],"best":[121],"knowledge,":[124],"method":[129],"not":[131],"yet":[132],"been":[133],"explored":[134],"IVMOPs.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}