{"id":"https://openalex.org/W1971509874","doi":"https://doi.org/10.1007/s10957-012-0144-0","title":"Adjoint Coexhausters in Nonsmooth Analysis and Extremality Conditions","display_name":"Adjoint Coexhausters in Nonsmooth Analysis and Extremality Conditions","publication_year":2012,"publication_date":"2012-08-07","ids":{"openalex":"https://openalex.org/W1971509874","doi":"https://doi.org/10.1007/s10957-012-0144-0","mag":"1971509874"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-012-0144-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0144-0","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/A5087691744","display_name":"Majid E. Abbasov","orcid":"https://orcid.org/0000-0003-1484-4733"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"M. E. Abbasov","raw_affiliation_strings":["Saint Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, Russia","Saint\u2010Petersburg State University St.\u00a0Petersburg Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saint Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Saint\u2010Petersburg State University St.\u00a0Petersburg Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026886870","display_name":"V. F. Demyanov","orcid":"https://orcid.org/0000-0002-2164-1232"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. F. Demyanov","raw_affiliation_strings":["Saint Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, Russia","Saint\u2010Petersburg State University St.\u00a0Petersburg Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saint Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Saint\u2010Petersburg State University St.\u00a0Petersburg Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087691744"],"corresponding_institution_ids":["https://openalex.org/I172901346"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3473,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.59552768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"156","issue":"3","first_page":"535","last_page":"553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9900000095367432,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9869999885559082,"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/mathematics","display_name":"Mathematics","score":0.882198691368103},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7071857452392578},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.6779999732971191},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.6737073659896851},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5583639144897461},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5518569946289062},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5219594836235046},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5097634196281433},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49101924896240234},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4776950180530548},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.47453129291534424},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.47133874893188477},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45893168449401855},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4516597390174866},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.437344491481781},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.41901424527168274},{"id":"https://openalex.org/keywords/pseudoconvex-function","display_name":"Pseudoconvex function","score":0.4172613024711609},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3890722393989563},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.38595831394195557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25929394364356995},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.22252485156059265},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11198210716247559},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08448964357376099}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.882198691368103},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7071857452392578},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.6779999732971191},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.6737073659896851},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5583639144897461},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5518569946289062},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5219594836235046},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5097634196281433},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49101924896240234},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4776950180530548},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.47453129291534424},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.47133874893188477},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45893168449401855},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4516597390174866},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.437344491481781},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.41901424527168274},{"id":"https://openalex.org/C118888059","wikidata":"https://www.wikidata.org/wiki/Q7254692","display_name":"Pseudoconvex function","level":5,"score":0.4172613024711609},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3890722393989563},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.38595831394195557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25929394364356995},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.22252485156059265},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11198210716247559},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08448964357376099},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-012-0144-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0144-0","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"},{"id":"pmh:oai:RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0144-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-012-0144-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.6299999952316284,"display_name":"Climate action"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W70607491","https://openalex.org/W127538475","https://openalex.org/W165344703","https://openalex.org/W574400632","https://openalex.org/W574530615","https://openalex.org/W1971921067","https://openalex.org/W1975549799","https://openalex.org/W1988527349","https://openalex.org/W2020501805","https://openalex.org/W2030269633","https://openalex.org/W2050930406","https://openalex.org/W2070024513","https://openalex.org/W2168078917","https://openalex.org/W2325681654","https://openalex.org/W2327535757","https://openalex.org/W2575619325","https://openalex.org/W3106807711","https://openalex.org/W4249667877","https://openalex.org/W4254505840","https://openalex.org/W6629818200"],"related_works":["https://openalex.org/W2064205779","https://openalex.org/W2377750169","https://openalex.org/W2356261519","https://openalex.org/W2072707988","https://openalex.org/W2364861597","https://openalex.org/W2356958610","https://openalex.org/W2048540358","https://openalex.org/W4251788152","https://openalex.org/W2994847349","https://openalex.org/W3020982396"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}