{"id":"https://openalex.org/W1965293593","doi":"https://doi.org/10.1007/s10898-013-0057-y","title":"New methods for calculating $$\\alpha $$ BB-type underestimators","display_name":"New methods for calculating $$\\alpha $$ BB-type underestimators","publication_year":2013,"publication_date":"2013-04-01","ids":{"openalex":"https://openalex.org/W1965293593","doi":"https://doi.org/10.1007/s10898-013-0057-y","mag":"1965293593"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-013-0057-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-013-0057-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","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/A5062185316","display_name":"Anders Skj\u00e4l","orcid":null},"institutions":[{"id":"https://openalex.org/I130217899","display_name":"\u00c5bo Akademi University","ror":"https://ror.org/029pk6x14","country_code":"FI","type":"education","lineage":["https://openalex.org/I130217899"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Anders Skj\u00e4l","raw_affiliation_strings":["Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, Biskopsgatan 8, 20500 , \u00c5bo, Finland","Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, \u00c5bo, Finland 20500#TAB#"],"affiliations":[{"raw_affiliation_string":"Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, Biskopsgatan 8, 20500 , \u00c5bo, Finland","institution_ids":["https://openalex.org/I130217899"]},{"raw_affiliation_string":"Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, \u00c5bo, Finland 20500#TAB#","institution_ids":["https://openalex.org/I130217899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037388244","display_name":"Tapio Westerlund","orcid":"https://orcid.org/0000-0002-8979-9642"},"institutions":[{"id":"https://openalex.org/I130217899","display_name":"\u00c5bo Akademi University","ror":"https://ror.org/029pk6x14","country_code":"FI","type":"education","lineage":["https://openalex.org/I130217899"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Tapio Westerlund","raw_affiliation_strings":["Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, Biskopsgatan 8, 20500 , \u00c5bo, Finland","Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, \u00c5bo, Finland 20500#TAB#"],"affiliations":[{"raw_affiliation_string":"Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, Biskopsgatan 8, 20500 , \u00c5bo, Finland","institution_ids":["https://openalex.org/I130217899"]},{"raw_affiliation_string":"Center of Excellence in Optimization and Systems Engineering, \u00c5bo Akademi University, \u00c5bo, Finland 20500#TAB#","institution_ids":["https://openalex.org/I130217899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062185316"],"corresponding_institution_ids":["https://openalex.org/I130217899"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":2.9837,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.90540195,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"3","first_page":"411","last_page":"427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9966999888420105,"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":0.880066454410553},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7893991470336914},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6048790216445923},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5817424058914185},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5384379029273987},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5034975409507751},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4968610107898712},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4802411198616028},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4661703407764435},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.4642788767814636},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41978058218955994},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.41699302196502686},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3496454954147339},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3237192928791046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.254389226436615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1662716567516327},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08861139416694641}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.880066454410553},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7893991470336914},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6048790216445923},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5817424058914185},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5384379029273987},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5034975409507751},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4968610107898712},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4802411198616028},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4661703407764435},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.4642788767814636},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41978058218955994},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.41699302196502686},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3496454954147339},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3237192928791046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.254389226436615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1662716567516327},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08861139416694641},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-013-0057-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-013-0057-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:58:y:2014:i:3:p:411-427","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-013-0057-y","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":null,"raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/e1df1207-9440-49a4-996d-d89a081108f8","is_oa":false,"landing_page_url":"https://research.abo.fi/en/publications/e1df1207-9440-49a4-996d-d89a081108f8","pdf_url":null,"source":{"id":"https://openalex.org/S4406923060","display_name":"\u00c5bo Akademi University Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Skj\u00e4l, A & Westerlund, T 2014, 'New methods for calculating \u03b1 BB-type underestimators', Journal of Global Optimization, vol. 58, no. 3, pp. 411\u2013427. https://doi.org/10.1007/s10898-013-0057-y","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324828","display_name":"\u00c5bo Akademi","ror":null},{"id":"https://openalex.org/F4320327732","display_name":"Walter Ahlstr\u00f6min S\u00e4\u00e4ti\u00f6","ror":"https://ror.org/00vdff906"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W107512677","https://openalex.org/W114465074","https://openalex.org/W182352379","https://openalex.org/W200606222","https://openalex.org/W1483874187","https://openalex.org/W1502865462","https://openalex.org/W1511572470","https://openalex.org/W1558506607","https://openalex.org/W1563737017","https://openalex.org/W1578255396","https://openalex.org/W1606844664","https://openalex.org/W1966523142","https://openalex.org/W1966593072","https://openalex.org/W1967710355","https://openalex.org/W1981009968","https://openalex.org/W1984425167","https://openalex.org/W1988622494","https://openalex.org/W1994143266","https://openalex.org/W2032234281","https://openalex.org/W2061143109","https://openalex.org/W2061951988","https://openalex.org/W2073605101","https://openalex.org/W2084006722","https://openalex.org/W2094654075","https://openalex.org/W2112289054","https://openalex.org/W2117060314","https://openalex.org/W2293000863","https://openalex.org/W2296319761","https://openalex.org/W2330548796","https://openalex.org/W2894871027","https://openalex.org/W3146520007","https://openalex.org/W4237717322","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2990487117","https://openalex.org/W2012882356","https://openalex.org/W4297883503","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2085275338","https://openalex.org/W2377262226","https://openalex.org/W4285295794","https://openalex.org/W2098412892"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
