{"id":"https://openalex.org/W30143669","doi":"https://doi.org/10.1023/a:1010957515360","title":"Contingent Derivatives of Implicit (Multi-) Functions and Stationary Points","display_name":"Contingent Derivatives of Implicit (Multi-) Functions and Stationary Points","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W30143669","doi":"https://doi.org/10.1023/a:1010957515360","mag":"30143669"},"language":"en","primary_location":{"id":"doi:10.1023/a:1010957515360","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1010957515360","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","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/A5040898115","display_name":"Diethard Klatte","orcid":"https://orcid.org/0000-0003-1859-3249"},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Diethard Klatte","raw_affiliation_strings":["Institut f\u00fcr Operations Research der Universit\u00e4t Z\u00fcrich, CH-8044, Z\u00fcrich, Switzerland","Institut f\u00fcr Operations Research der Universit\u00e4t Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Operations Research der Universit\u00e4t Z\u00fcrich, CH-8044, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I202697423"]},{"raw_affiliation_string":"Institut f\u00fcr Operations Research der Universit\u00e4t Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040277337","display_name":"Bernd Kummer","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernd Kummer","raw_affiliation_strings":["Institut f\u00fcr Mathematik der Humboldt-Universit\u00e4t Berlin, D-10099, Berlin, Germany","Institut f\u00fcr Mathematik der Humboldt-Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik der Humboldt-Universit\u00e4t Berlin, D-10099, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik der Humboldt-Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.8876,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70885229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"101","issue":"1-4","first_page":"313","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9876999855041504,"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/theory-of-computation","display_name":"Theory of computation","score":0.7850950956344604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6257718205451965},{"id":"https://openalex.org/keywords/implicit-function-theorem","display_name":"Implicit function theorem","score":0.6064613461494446},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6058297753334045},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5285155773162842},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5011470317840576},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4983341693878174},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4765737056732178},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4449959993362427},{"id":"https://openalex.org/keywords/continuous-function","display_name":"Continuous function (set theory)","score":0.43673816323280334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41465187072753906},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3589756488800049},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3409198522567749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3216736912727356},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23596319556236267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18406736850738525},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13911357522010803},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06181463599205017}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7850950956344604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6257718205451965},{"id":"https://openalex.org/C138578839","wikidata":"https://www.wikidata.org/wiki/Q848375","display_name":"Implicit function theorem","level":2,"score":0.6064613461494446},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6058297753334045},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5285155773162842},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5011470317840576},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4983341693878174},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4765737056732178},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4449959993362427},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.43673816323280334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41465187072753906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3589756488800049},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3409198522567749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3216736912727356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23596319556236267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18406736850738525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13911357522010803},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06181463599205017},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1023/a:1010957515360","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1010957515360","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:annopr:v:101:y:2001:i:1:p:313-331:10.1023/a:1010957515360","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1023/A:1010957515360","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W109144975","https://openalex.org/W1484024929","https://openalex.org/W1583089965","https://openalex.org/W1601741115","https://openalex.org/W1607072065","https://openalex.org/W1967784957","https://openalex.org/W1993647205","https://openalex.org/W2000125728","https://openalex.org/W2003292231","https://openalex.org/W2014746566","https://openalex.org/W2022853838","https://openalex.org/W2023105568","https://openalex.org/W2027378843","https://openalex.org/W2032449980","https://openalex.org/W2033155834","https://openalex.org/W2033560262","https://openalex.org/W2036613704","https://openalex.org/W2046005535","https://openalex.org/W2057361274","https://openalex.org/W2065846434","https://openalex.org/W2073329629","https://openalex.org/W2076627354","https://openalex.org/W2081698249","https://openalex.org/W2497608796"],"related_works":["https://openalex.org/W4250775169","https://openalex.org/W4309231192","https://openalex.org/W2064563243","https://openalex.org/W2351452215","https://openalex.org/W2381413256","https://openalex.org/W2617963432","https://openalex.org/W3165104833","https://openalex.org/W2012783289","https://openalex.org/W2018678701","https://openalex.org/W2376959945"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}
