{"id":"https://openalex.org/W2067250331","doi":"https://doi.org/10.1007/bf01581278","title":"D.c. sets, d.c. functions and nonlinear equations","display_name":"D.c. sets, d.c. functions and nonlinear equations","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2067250331","doi":"https://doi.org/10.1007/bf01581278","mag":"2067250331"},"language":"en","primary_location":{"id":"doi:10.1007/bf01581278","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01581278","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/A5041708435","display_name":"Phan Thi\u00ean Thach","orcid":null},"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":true,"raw_author_name":"Phan Thien Thach","raw_affiliation_strings":["Institute of Mathematics, Hanoi, Viet Nam","Institute of Mathematics, Hanoi, Viet Nam#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hanoi, Viet Nam","institution_ids":["https://openalex.org/I4210148301"]},{"raw_affiliation_string":"Institute of Mathematics, Hanoi, Viet Nam#TAB#","institution_ids":["https://openalex.org/I4210148301"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041708435"],"corresponding_institution_ids":["https://openalex.org/I4210148301"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.821,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.917,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"1-3","first_page":"415","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9972000122070312,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.987500011920929,"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/mathematics","display_name":"Mathematics","score":0.8470532894134521},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5658908486366272},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5353679060935974},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5036959052085876},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4729844331741333},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4705386757850647},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43081653118133545},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4296151399612427},{"id":"https://openalex.org/keywords/universality","display_name":"Universality (dynamical systems)","score":0.4257325530052185},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4126850366592407},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3939823508262634},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34818270802497864},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.21052861213684082},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15092593431472778}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8470532894134521},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5658908486366272},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5353679060935974},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5036959052085876},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4729844331741333},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4705386757850647},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43081653118133545},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4296151399612427},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.4257325530052185},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4126850366592407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3939823508262634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34818270802497864},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21052861213684082},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15092593431472778},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01581278","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01581278","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":[{"id":"https://openalex.org/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W44939114","https://openalex.org/W160520070","https://openalex.org/W331442585","https://openalex.org/W362586008","https://openalex.org/W1965134187","https://openalex.org/W1968707428","https://openalex.org/W1994795725","https://openalex.org/W1996239617","https://openalex.org/W2002603218","https://openalex.org/W2023054591","https://openalex.org/W2059690973","https://openalex.org/W2081674331","https://openalex.org/W2082736860","https://openalex.org/W2116403087","https://openalex.org/W2135154756","https://openalex.org/W2186273234","https://openalex.org/W3215382836","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W2187391117","https://openalex.org/W4327738859","https://openalex.org/W1981809986","https://openalex.org/W1843467136","https://openalex.org/W2949367465","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W3029201158","https://openalex.org/W1996226968"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}