{"id":"https://openalex.org/W7130323353","doi":"https://doi.org/10.1007/s10957-026-02941-3","title":"On Projectional Subdifferentials and Projectional Coderivatives with Respect to Smooth Manifolds","display_name":"On Projectional Subdifferentials and Projectional Coderivatives with Respect to Smooth Manifolds","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130323353","doi":"https://doi.org/10.1007/s10957-026-02941-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-02941-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02941-3","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/A5059731357","display_name":"Phan Qu\u1ed1c Kh\u00e1nh","orcid":"https://orcid.org/0000-0002-0524-0498"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Phan Quoc Khanh","raw_affiliation_strings":["Analytical and Algebraic Methods in Optimization Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Analytical and Algebraic Methods in Optimization Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126328723","display_name":"Tran Tuan Minh","orcid":null},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]},{"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":false,"raw_author_name":"Tran Tuan Minh","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), Ho Chi Minh City, Vietnam","Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I47265099"]},{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059731357"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"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":0.65075197,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"208","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.2378000020980835,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.2378000020980835,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.17329999804496765,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.06639999896287918,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/function","display_name":"Function (biology)","score":0.5217000246047974},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5095000267028809},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.48840001225471497},{"id":"https://openalex.org/keywords/meaning","display_name":"Meaning (existential)","score":0.3785000145435333},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.3122999966144562}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.746999979019165},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5217000246047974},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5095000267028809},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.461899995803833},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.349700003862381},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.24120000004768372},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.22040000557899475}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10957-026-02941-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02941-3","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":"Reduced inequalities","score":0.6246914863586426,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1557324374","https://openalex.org/W1966627654","https://openalex.org/W1985368200","https://openalex.org/W2046019310","https://openalex.org/W2061455579","https://openalex.org/W2141519660","https://openalex.org/W2312877741","https://openalex.org/W2797479470","https://openalex.org/W2885473730","https://openalex.org/W3088389032","https://openalex.org/W4249513058","https://openalex.org/W4323539420","https://openalex.org/W4385576829","https://openalex.org/W4388105626"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-20T06:14:18.993340","created_date":"2026-02-19T00:00:00"}
