{"id":"https://openalex.org/W7196995116","doi":"https://doi.org/10.1007/s10957-026-03064-5","title":"Clarke-Type Directional Derivatives and their Applications to Generalized Convexity and Optimality Conditions in Non-Lipschitz Settings","display_name":"Clarke-Type Directional Derivatives and their Applications to Generalized Convexity and Optimality Conditions in Non-Lipschitz Settings","publication_year":2026,"publication_date":"2026-08-01","ids":{"openalex":"https://openalex.org/W7196995116","doi":"https://doi.org/10.1007/s10957-026-03064-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-03064-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03064-5","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/A5009459697","display_name":"Minh T\u00f9ng Nguy\u1ec5n","orcid":"https://orcid.org/0000-0001-6314-6013"},"institutions":[{"id":"https://openalex.org/I3129629310","display_name":"Ho Chi Minh University of Banking","ror":"https://ror.org/03fsckq75","country_code":"VN","type":"education","lineage":["https://openalex.org/I3129629310"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Minh Tung Nguyen","raw_affiliation_strings":["Faculty of Data Science of Business, Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Data Science of Business, Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I3129629310"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5145670418","display_name":"Xuan Duy Bao Nguyen","orcid":"https://orcid.org/0009-0005-3767-9306"},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I47265099","display_name":"Ho Chi Minh City University of Technology","ror":"https://ror.org/04qva2324","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I47265099"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Xuan Duy Bao Nguyen","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, Dien Hong Ward, Ho Chi Minh City, Vietnam","Vietnam National University Ho Chi Minh City, Linh Xuan Ward, Ho Chi Minh City, Vietnam"],"raw_orcid":"https://orcid.org/0009-0005-3767-9306","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, Dien Hong Ward, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I47265099"]},{"raw_affiliation_string":"Vietnam National University Ho Chi Minh City, Linh Xuan Ward, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5145670418"],"corresponding_institution_ids":["https://openalex.org/I123565023","https://openalex.org/I47265099"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85953505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"210","issue":"2","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":0.9175999760627747,"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":0.9175999760627747,"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":0.01269999984651804,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.006300000008195639,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/convexity","display_name":"Convexity","score":0.75},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6270999908447266},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.37310001254081726},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.31779998540878296},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.2919999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7680000066757202},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.75},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49000000953674316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4246000051498413},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2919999957084656},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.24899999797344208},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.24899999797344208}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10957-026-03064-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03064-5","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":[{"display_name":"Climate action","score":0.40151312947273254,"id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G5966624687","display_name":"Nghi\u00ean c\u1ee9u m\u1ed9t s\u1ed1 k\u1ef9 thu\u1eadt m\u1edbi trong gi\u1ea3i t\u00edch bi\u1ebfn ph\u00e2n v\u00e0 \u1ee9ng d\u1ee5ng trong t\u1ed1i \u01b0u h\u00f3a","funder_award_id":"101.01-2025.14","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1545461878","https://openalex.org/W1551360398","https://openalex.org/W1574936051","https://openalex.org/W1601741115","https://openalex.org/W1967069096","https://openalex.org/W1972617480","https://openalex.org/W1981928753","https://openalex.org/W1993613781","https://openalex.org/W2000985550","https://openalex.org/W2003540223","https://openalex.org/W2024279814","https://openalex.org/W2025475099","https://openalex.org/W2027449074","https://openalex.org/W2053616442","https://openalex.org/W2061114984","https://openalex.org/W2066286387","https://openalex.org/W2083759756","https://openalex.org/W2097273628","https://openalex.org/W2110041091","https://openalex.org/W2122856151","https://openalex.org/W2168346106","https://openalex.org/W2478963760","https://openalex.org/W2494957067","https://openalex.org/W2557779326","https://openalex.org/W2885473730","https://openalex.org/W2893667449","https://openalex.org/W2912430942","https://openalex.org/W3009136763","https://openalex.org/W4252261227","https://openalex.org/W4381741434","https://openalex.org/W4401522050","https://openalex.org/W4409172841"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-08-07T00:00:00"}