{"id":"https://openalex.org/W1989095807","doi":"https://doi.org/10.1007/bf02614516","title":"On the degree and separability of nonconvexity and applications to optimization problems","display_name":"On the degree and separability of nonconvexity and applications to optimization problems","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W1989095807","doi":"https://doi.org/10.1007/bf02614516","mag":"1989095807"},"language":"en","primary_location":{"id":"doi:10.1007/bf02614516","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02614516","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"]},{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP","VN"],"is_corresponding":true,"raw_author_name":"Phan Thien Thach","raw_affiliation_strings":["Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Oh-Okayama. Megoro-ku, 152, Tokyo, Japan","Institute of Mathematics, Hanoi, Viet Nam"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Oh-Okayama. Megoro-ku, 152, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]},{"raw_affiliation_string":"Institute of Mathematics, Hanoi, Viet Nam","institution_ids":["https://openalex.org/I4210148301"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001687718","display_name":"Hiroshi Konno","orcid":"https://orcid.org/0000-0003-4784-1483"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Konno","raw_affiliation_strings":["Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Oh-Okayama. Megoro-ku, 152, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Oh-Okayama. Megoro-ku, 152, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041708435"],"corresponding_institution_ids":["https://openalex.org/I114531698","https://openalex.org/I4210148301"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.5161,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.62782262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"77","issue":"3","first_page":"23","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9973999857902527,"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":0.9973999857902527,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9918000102043152,"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":0.7670111656188965},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6351143717765808},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6036388874053955},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5797880291938782},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5343109369277954},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4948400855064392},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4681406617164612},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4651672840118408},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4397083520889282},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3600079417228699},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23332759737968445},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21675166487693787},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16269975900650024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13837841153144836},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07553163170814514}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670111656188965},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6351143717765808},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6036388874053955},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5797880291938782},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5343109369277954},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4948400855064392},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4681406617164612},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4651672840118408},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4397083520889282},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3600079417228699},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23332759737968445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21675166487693787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16269975900650024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13837841153144836},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07553163170814514},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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":2,"locations":[{"id":"doi:10.1007/bf02614516","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02614516","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"},{"id":"pmh:oai:ddd.uab.cat:68","is_oa":false,"landing_page_url":"https://ddd.uab.cat/record/68","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1499399028","https://openalex.org/W1547127570","https://openalex.org/W1653619892","https://openalex.org/W1968143987","https://openalex.org/W1976587341","https://openalex.org/W1985534288","https://openalex.org/W1989313814","https://openalex.org/W1993247264","https://openalex.org/W1996239617","https://openalex.org/W2000354435","https://openalex.org/W2024615944","https://openalex.org/W2034713829","https://openalex.org/W2035567981","https://openalex.org/W2057655209","https://openalex.org/W2062058089","https://openalex.org/W2065704444","https://openalex.org/W2067250331","https://openalex.org/W2078470842","https://openalex.org/W2093678960","https://openalex.org/W2100440346","https://openalex.org/W2142506503","https://openalex.org/W2170675987","https://openalex.org/W2186273234","https://openalex.org/W2505968561","https://openalex.org/W4246092883","https://openalex.org/W4249667877","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W2168900540","https://openalex.org/W2125310826","https://openalex.org/W2380536887","https://openalex.org/W4244456529"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
