{"id":"https://openalex.org/W7163931006","doi":"https://doi.org/10.1016/j.cam.2026.117864","title":"A nonmonotone Polak-Ribi\u00e8re-Polyak conjugate gradient method for multiobjective optimization problems","display_name":"A nonmonotone Polak-Ribi\u00e8re-Polyak conjugate gradient method for multiobjective optimization problems","publication_year":2026,"publication_date":"2026-06-08","ids":{"openalex":"https://openalex.org/W7163931006","doi":"https://doi.org/10.1016/j.cam.2026.117864"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2026.117864","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2026.117864","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","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/A5022567076","display_name":"Ashutosh Upadhayay","orcid":null},"institutions":[{"id":"https://openalex.org/I139858224","display_name":"M.J.P. Rohilkhand University","ror":"https://ror.org/02e3nay30","country_code":"IN","type":"education","lineage":["https://openalex.org/I139858224"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ashutosh Upadhayay","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221 005, India","Department of Mathematics, Bareilly College, Bareilly, Uttar Pradesh, 243005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221 005, India","institution_ids":["https://openalex.org/I91357014"]},{"raw_affiliation_string":"Department of Mathematics, Bareilly College, Bareilly, Uttar Pradesh, 243005, India","institution_ids":["https://openalex.org/I139858224"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138155501","display_name":"Debdas Ghosh","orcid":null},"institutions":[{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debdas Ghosh","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221 005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221 005, India","institution_ids":["https://openalex.org/I91357014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138154677","display_name":"Qamrul Hasan Ansari","orcid":"https://orcid.org/0000-0002-0707-7372"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Qamrul Hasan Ansari","raw_affiliation_strings":["Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0707-7372","affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138143789","display_name":"Jen-Chih Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":["Center for General Education, China Medical University, Taichung, 40402, Taiwan","Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University, Taichung, 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]},{"raw_affiliation_string":"Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan","institution_ids":["https://openalex.org/I142974352"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5138123884","display_name":"Xiaopeng Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I198091727","display_name":"Tiangong University","ror":"https://ror.org/00xsr9m91","country_code":"CN","type":"education","lineage":["https://openalex.org/I198091727"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaopeng Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China","institution_ids":["https://openalex.org/I198091727"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5138154677"],"corresponding_institution_ids":["https://openalex.org/I134085113"],"apc_list":{"value":3040,"currency":"USD","value_usd":2870},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.72110681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"489","issue":null,"first_page":"117864","last_page":"117864"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.5217999815940857,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.5217999815940857,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.3003000020980835,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0706000030040741,"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7124000191688538},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.5084999799728394},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5009999871253967},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4878000020980835},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.37720000743865967},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3637000024318695},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.3531000018119812}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8303999900817871},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7124000191688538},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5234000086784363},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.5084999799728394},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5009999871253967},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4918999969959259},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.37720000743865967},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.3531000018119812},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C2988952207","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multiobjective programming","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cam.2026.117864","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2026.117864","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1606015457","https://openalex.org/W1975335027","https://openalex.org/W1980432290","https://openalex.org/W2004586020","https://openalex.org/W2012231377","https://openalex.org/W2014851363","https://openalex.org/W2018215034","https://openalex.org/W2043430160","https://openalex.org/W2064006173","https://openalex.org/W2066743741","https://openalex.org/W2091549324","https://openalex.org/W2100717205","https://openalex.org/W2143185749","https://openalex.org/W2149454052","https://openalex.org/W2167137033","https://openalex.org/W2316564661","https://openalex.org/W2618176816","https://openalex.org/W2893010165","https://openalex.org/W2960169247","https://openalex.org/W2981335079","https://openalex.org/W3155049830","https://openalex.org/W3194711412","https://openalex.org/W4210731468","https://openalex.org/W4285731255","https://openalex.org/W4296182520","https://openalex.org/W4376648257","https://openalex.org/W4391160797","https://openalex.org/W4401011563","https://openalex.org/W4403514089","https://openalex.org/W4405886640"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-06-09T00:00:00"}