{"id":"https://openalex.org/W2055448128","doi":"https://doi.org/10.1007/s10107-007-0120-x","title":"Subgradients of marginal functions in parametric mathematical programming","display_name":"Subgradients of marginal functions in parametric mathematical programming","publication_year":2007,"publication_date":"2007-04-27","ids":{"openalex":"https://openalex.org/W2055448128","doi":"https://doi.org/10.1007/s10107-007-0120-x","mag":"2055448128"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-007-0120-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0120-x","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"B. S. Mordukhovich","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","Wayne State University, Department of Mathematics, 48202, Detroit, MI, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Wayne State University, Department of Mathematics, 48202, Detroit, MI, USA#TAB#","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002094273","display_name":"Nguyen Mau Nam","orcid":"https://orcid.org/0000-0003-4850-2301"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. M. Nam","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","Wayne State University, Department of Mathematics, 48202, Detroit, MI, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Wayne State University, Department of Mathematics, 48202, Detroit, MI, USA#TAB#","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061405938","display_name":"N. D. Yen","orcid":"https://orcid.org/0000-0001-7250-7933"},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"N. D. Yen","raw_affiliation_strings":["Institute of Mathematics, 18 Hoang Quoc Viet Rd., 10307, Hanoi, Vietnam","Institute of Mathematics, 18 Hoang Quoc Viet Rd., 10307, Hanoi, MI, Vietnam#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, 18 Hoang Quoc Viet Rd., 10307, Hanoi, Vietnam","institution_ids":["https://openalex.org/I4210148301"]},{"raw_affiliation_string":"Institute of Mathematics, 18 Hoang Quoc Viet Rd., 10307, Hanoi, MI, Vietnam#TAB#","institution_ids":["https://openalex.org/I4210148301"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066241737"],"corresponding_institution_ids":["https://openalex.org/I185443292"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":6.3954,"has_fulltext":false,"cited_by_count":156,"citation_normalized_percentile":{"value":0.96742658,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"116","issue":"1-2","first_page":"369","last_page":"396"},"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9937999844551086,"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/mathematics","display_name":"Mathematics","score":0.8262643218040466},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7257824540138245},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.6481601595878601},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6297276616096497},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5905786156654358},{"id":"https://openalex.org/keywords/parametric-programming","display_name":"Parametric programming","score":0.5127030611038208},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5102932453155518},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4722442030906677},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46234551072120667},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4540357291698456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42963361740112305},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42104029655456543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17299997806549072},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11474579572677612}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8262643218040466},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7257824540138245},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6481601595878601},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6297276616096497},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5905786156654358},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.5127030611038208},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5102932453155518},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4722442030906677},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46234551072120667},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4540357291698456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42963361740112305},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42104029655456543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17299997806549072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11474579572677612},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-007-0120-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0120-x","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W171887514","https://openalex.org/W193697020","https://openalex.org/W197936677","https://openalex.org/W217831350","https://openalex.org/W345014192","https://openalex.org/W615848585","https://openalex.org/W1492700492","https://openalex.org/W1493492050","https://openalex.org/W1499439642","https://openalex.org/W1528330203","https://openalex.org/W1551360398","https://openalex.org/W1601741115","https://openalex.org/W1601960826","https://openalex.org/W1604627832","https://openalex.org/W1966129445","https://openalex.org/W1977538235","https://openalex.org/W1984528929","https://openalex.org/W2015570398","https://openalex.org/W2045940260","https://openalex.org/W2049565231","https://openalex.org/W2057578212","https://openalex.org/W2081790609","https://openalex.org/W2091992858","https://openalex.org/W2097287227","https://openalex.org/W2136953603","https://openalex.org/W2149409914","https://openalex.org/W2153562582","https://openalex.org/W2239070540","https://openalex.org/W2869708730","https://openalex.org/W2955198501","https://openalex.org/W3157341860","https://openalex.org/W4231147659","https://openalex.org/W4238293458","https://openalex.org/W4245086370","https://openalex.org/W4249513058","https://openalex.org/W4250028192","https://openalex.org/W4285719527","https://openalex.org/W4299815621","https://openalex.org/W6611554589","https://openalex.org/W6629610695","https://openalex.org/W6632629376"],"related_works":["https://openalex.org/W170645000","https://openalex.org/W2268772487","https://openalex.org/W1493833140","https://openalex.org/W2019098589","https://openalex.org/W105343188","https://openalex.org/W1976680397","https://openalex.org/W2021900925","https://openalex.org/W2803122527","https://openalex.org/W313145056","https://openalex.org/W2759527253"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":16}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
