{"id":"https://openalex.org/W2095843220","doi":"https://doi.org/10.1287/moor.10.4.612","title":"A Note on Differentiability of Global Optimal Values","display_name":"A Note on Differentiability of Global Optimal Values","publication_year":1985,"publication_date":"1985-11-01","ids":{"openalex":"https://openalex.org/W2095843220","doi":"https://doi.org/10.1287/moor.10.4.612","mag":"2095843220"},"language":"en","primary_location":{"id":"doi:10.1287/moor.10.4.612","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.10.4.612","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics 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/A5022679054","display_name":"Okitsugu Fujiwara","orcid":null},"institutions":[{"id":"https://openalex.org/I38538140","display_name":"Asian Institute of Technology","ror":"https://ror.org/0403qcr87","country_code":"TH","type":"education","lineage":["https://openalex.org/I38538140"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Okitsugu Fujiwara","raw_affiliation_strings":["Industrial Engineering and Management Division, Asian Institute of Technology, P.O.B. 2754, Bangkok, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Engineering and Management Division, Asian Institute of Technology, P.O.B. 2754, Bangkok, Thailand","institution_ids":["https://openalex.org/I38538140"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022679054"],"corresponding_institution_ids":["https://openalex.org/I38538140"],"apc_list":null,"apc_paid":null,"fwci":2.3636,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89122089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"4","first_page":"612","last_page":"618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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":0.978600025177002,"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":0.9674999713897705,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8937574028968811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.881184458732605},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5499621033668518},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5086804032325745},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4904915988445282},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.47823208570480347},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46854910254478455},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4569980502128601},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4565356373786926},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41020241379737854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08689010143280029}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8937574028968811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.881184458732605},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5499621033668518},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5086804032325745},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4904915988445282},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.47823208570480347},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46854910254478455},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4569980502128601},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4565356373786926},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41020241379737854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08689010143280029},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1287/moor.10.4.612","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.10.4.612","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:inm:ormoor:v:10:y:1985:i:4:p:612-618","is_oa":false,"landing_page_url":"http://doi.org/10.1287/moor.10.4.612","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":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1974109775","https://openalex.org/W2052731183","https://openalex.org/W2128399853"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W4252812829","https://openalex.org/W4309796600","https://openalex.org/W4353106425"],"abstract_inverted_index":{"The":[0,17],"differentiability":[1],"of":[2,28,52,59,69],"global":[3,39],"optimal":[4,40],"values":[5],"for":[6],"smooth":[7],"constrained":[8],"programs":[9],"with":[10,46],"respect":[11,47],"to":[12,25,48,63],"general":[13],"perturbations":[14],"is":[15,23,42],"considered.":[16],"strong":[18],"Whitney":[19],"C":[20],"2":[21],"-topology":[22],"used":[24],"the":[26,38,49],"space":[27,51],"objective":[29,53,66],"functions":[30,54],"and":[31,55],"constraints.":[32,56],"It":[33],"will":[34],"be":[35],"shown":[36],"generically":[37],"value":[41],"twice":[43],"continuously":[44],"differentiable":[45],"function":[50,68],"An":[57],"application":[58],"this":[60],"genericity":[61],"argument":[62],"a":[64],"nonsmooth":[65],"function\u2014a":[67],"maximum":[70],"type\u2014is":[71],"also":[72],"discussed.":[73]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
