{"id":"https://openalex.org/W1980840035","doi":"https://doi.org/10.1007/bf01415887","title":"On generalized gradients","display_name":"On generalized gradients","publication_year":1992,"publication_date":"1992-05-01","ids":{"openalex":"https://openalex.org/W1980840035","doi":"https://doi.org/10.1007/bf01415887","mag":"1980840035"},"language":"en","primary_location":{"id":"doi:10.1007/bf01415887","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01415887","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"ZOR Zeitschrift f\ufffdr Operations Research Methods and Models 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/A5071256938","display_name":"Peter Recht","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"P. Recht","raw_affiliation_strings":["Institute of Statistics and Mathematical Economics, University of Karlsruhe, P.O.Box 6980, D-7500, Karlsruhe, Germany","University of Karlsruhe#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Statistics and Mathematical Economics, University of Karlsruhe, P.O.Box 6980, D-7500, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"University of Karlsruhe#TAB#","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071256938"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.052,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73394049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"3","first_page":"201","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9703999757766724,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9695000052452087,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8366109132766724},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7604161500930786},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.6171839237213135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5198979377746582},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5169567465782166},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4979372024536133},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.49329274892807007},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47626158595085144},{"id":"https://openalex.org/keywords/harmonics","display_name":"Harmonics","score":0.43476900458335876},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42415574193000793},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.416111558675766},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3625882565975189},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22979623079299927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17556580901145935}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8366109132766724},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7604161500930786},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.6171839237213135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5198979377746582},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5169567465782166},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4979372024536133},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.49329274892807007},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47626158595085144},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.43476900458335876},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42415574193000793},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.416111558675766},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3625882565975189},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22979623079299927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17556580901145935},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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":1,"locations":[{"id":"doi:10.1007/bf01415887","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01415887","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"ZOR Zeitschrift f\ufffdr Operations Research Methods and Models of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W40430404","https://openalex.org/W1551360398","https://openalex.org/W4240240566","https://openalex.org/W4243183471"],"related_works":["https://openalex.org/W3105173213","https://openalex.org/W2226784581","https://openalex.org/W942533424","https://openalex.org/W2097846334","https://openalex.org/W2049339417","https://openalex.org/W4255276256","https://openalex.org/W2531699496","https://openalex.org/W4301135054","https://openalex.org/W1968850685","https://openalex.org/W1506713792"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}