{"id":"https://openalex.org/W7140667603","doi":"https://doi.org/10.1007/s10957-026-02954-y","title":"Golden Ratio Algorithm with Inertia for Non-Lipschitz Variational Inequalities","display_name":"Golden Ratio Algorithm with Inertia for Non-Lipschitz Variational Inequalities","publication_year":2026,"publication_date":"2026-03-26","ids":{"openalex":"https://openalex.org/W7140667603","doi":"https://doi.org/10.1007/s10957-026-02954-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-02954-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02954-y","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","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/A5015615750","display_name":"Vahid Darvish","orcid":"https://orcid.org/0000-0001-8955-4007"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Vahid Darvish","raw_affiliation_strings":["Department of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076848804","display_name":"Godwin Chidi Ugwunnadi","orcid":"https://orcid.org/0000-0002-2711-7888"},"institutions":[{"id":"https://openalex.org/I101993903","display_name":"Namibia University of Science and Technology","ror":"https://ror.org/03gg1ey66","country_code":"NA","type":"education","lineage":["https://openalex.org/I101993903"]},{"id":"https://openalex.org/I2802393258","display_name":"Sefako Makgatho Health Sciences University","ror":"https://ror.org/003hsr719","country_code":"ZA","type":"education","lineage":["https://openalex.org/I2802393258"]}],"countries":["NA","ZA"],"is_corresponding":false,"raw_author_name":"Godwin Chidi Ugwunnadi","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, 0204, South Africa","Department of Mathematics, Statistics and Actuarial Science, Faculty of Health, Natural Resources and Applied Sciences, Namibia University of Science and Technology, Windhoek, Namibia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, 0204, South Africa","institution_ids":["https://openalex.org/I2802393258"]},{"raw_affiliation_string":"Department of Mathematics, Statistics and Actuarial Science, Faculty of Health, Natural Resources and Applied Sciences, Namibia University of Science and Technology, Windhoek, Namibia","institution_ids":["https://openalex.org/I101993903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091634339","display_name":"Aniefiok Udomene","orcid":null},"institutions":[{"id":"https://openalex.org/I98220444","display_name":"Michael Okpara University of Agriculture","ror":"https://ror.org/050850526","country_code":"NG","type":"education","lineage":["https://openalex.org/I98220444"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Aniefiok Udomene","raw_affiliation_strings":["Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Abia State, Nigeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Abia State, Nigeria","institution_ids":["https://openalex.org/I98220444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123737090","display_name":"Habib ur Rehman","orcid":null},"institutions":[{"id":"https://openalex.org/I120825670","display_name":"Yunnan Normal University","ror":"https://ror.org/00sc9n023","country_code":"CN","type":"education","lineage":["https://openalex.org/I120825670"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Habib ur Rehman","raw_affiliation_strings":["School of Mathematics, Yunnan Normal University, Kunming, 650092, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Yunnan Normal University, Kunming, 650092, P.R. China","institution_ids":["https://openalex.org/I120825670"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5123737090"],"corresponding_institution_ids":["https://openalex.org/I120825670"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.95050574,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"209","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.8334000110626221,"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":0.8334000110626221,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.07000000029802322,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.05260000005364418,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7736999988555908},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.7347999811172485},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7265999913215637},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7123000025749207},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.6998000144958496},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.6164000034332275},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"Golden ratio","score":0.5932999849319458},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.415800005197525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8260999917984009},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7736999988555908},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7347999811172485},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7265999913215637},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7123000025749207},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.6998000144958496},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.6164000034332275},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.5932999849319458},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4505999982357025},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.415800005197525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41200000047683716},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3652999997138977},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10957-026-02954-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02954-y","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5602454543113708,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1547403762","https://openalex.org/W1991765628","https://openalex.org/W1994910078","https://openalex.org/W2033310514","https://openalex.org/W2053487511","https://openalex.org/W2056743436","https://openalex.org/W2132528752","https://openalex.org/W2605652624","https://openalex.org/W2766745106","https://openalex.org/W2784200687","https://openalex.org/W2891266538","https://openalex.org/W2903821133","https://openalex.org/W2933689882","https://openalex.org/W2937942925","https://openalex.org/W2944073351","https://openalex.org/W2962762987","https://openalex.org/W2965900084","https://openalex.org/W2984057013","https://openalex.org/W3027831860","https://openalex.org/W3120218631","https://openalex.org/W3134443919","https://openalex.org/W3137879310","https://openalex.org/W3139279146","https://openalex.org/W3184464583","https://openalex.org/W4200474141","https://openalex.org/W4205234567","https://openalex.org/W4225320772","https://openalex.org/W4229650096","https://openalex.org/W4252789312","https://openalex.org/W4283212973","https://openalex.org/W4385199919","https://openalex.org/W4388468698","https://openalex.org/W4389046059","https://openalex.org/W4390810672","https://openalex.org/W4392955108","https://openalex.org/W4394064419","https://openalex.org/W4403467224","https://openalex.org/W4403552664"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-27T06:05:27.210665","created_date":"2026-03-27T00:00:00"}
