{"id":"https://openalex.org/W2944395221","doi":"https://doi.org/10.1007/s10898-019-00780-3","title":"Nonconvex min\u2013max fractional quadratic problems under quadratic constraints: copositive relaxations","display_name":"Nonconvex min\u2013max fractional quadratic problems under quadratic constraints: copositive relaxations","publication_year":2019,"publication_date":"2019-05-09","ids":{"openalex":"https://openalex.org/W2944395221","doi":"https://doi.org/10.1007/s10898-019-00780-3","mag":"2944395221"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-019-00780-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-019-00780-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-019-00780-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-019-00780-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091723931","display_name":"Paula Amaral","orcid":"https://orcid.org/0000-0002-0563-3443"},"institutions":[{"id":"https://openalex.org/I83558840","display_name":"Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89","country_code":"PT","type":"education","lineage":["https://openalex.org/I83558840"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Paula Alexandra Amaral","raw_affiliation_strings":["CMA and FCT, Universidade Nova de Lisboa, Lisbon, Portugal"],"raw_orcid":"https://orcid.org/0000-0002-0563-3443","affiliations":[{"raw_affiliation_string":"CMA and FCT, Universidade Nova de Lisboa, Lisbon, Portugal","institution_ids":["https://openalex.org/I83558840"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023776719","display_name":"Immanuel M. Bomze","orcid":"https://orcid.org/0000-0002-6288-9226"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Immanuel M. Bomze","raw_affiliation_strings":["ISOR/VCOR & ds:UniVie, Universit\u00e4t Wien, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISOR/VCOR & ds:UniVie, Universit\u00e4t Wien, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023776719"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.6489,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64098436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"75","issue":"2","first_page":"227","last_page":"245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9987000226974487,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9209831357002258},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7361140847206116},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4945525825023651},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4846968650817871},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40825995802879333},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.344501793384552},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33286821842193604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10383430123329163}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9209831357002258},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7361140847206116},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4945525825023651},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4846968650817871},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40825995802879333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.344501793384552},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33286821842193604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10383430123329163}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-019-00780-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-019-00780-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-019-00780-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:info:fedora/oai:univie.ac.at:o:1073065","is_oa":true,"landing_page_url":"https://phaidra.univie.ac.at/o:1073065","pdf_url":null,"source":{"id":"https://openalex.org/S4306401993","display_name":"Phaidra (Universit\u00e4t Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129774422","host_organization_name":"University of Vienna","host_organization_lineage":["https://openalex.org/I129774422"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0925-5001","raw_type":"article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:75:y:2019:i:2:d:10.1007_s10898-019-00780-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-019-00780-3","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"}],"best_oa_location":{"id":"doi:10.1007/s10898-019-00780-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-019-00780-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-019-00780-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5986682413","display_name":null,"funder_award_id":"UID/MAT/00297/2019","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2944395221.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1503386356","https://openalex.org/W1518832340","https://openalex.org/W1549791526","https://openalex.org/W1975552235","https://openalex.org/W1978504376","https://openalex.org/W1999765316","https://openalex.org/W1999913571","https://openalex.org/W2002358177","https://openalex.org/W2029650406","https://openalex.org/W2049679581","https://openalex.org/W2055751565","https://openalex.org/W2056779374","https://openalex.org/W2067171884","https://openalex.org/W2070643312","https://openalex.org/W2075855943","https://openalex.org/W2078600458","https://openalex.org/W2079135578","https://openalex.org/W2095393540","https://openalex.org/W2119326928","https://openalex.org/W2126138717","https://openalex.org/W2162579105","https://openalex.org/W2536620281","https://openalex.org/W3036596190","https://openalex.org/W3123166712","https://openalex.org/W4249759900","https://openalex.org/W4253679144"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3036464408","https://openalex.org/W2020990755","https://openalex.org/W2377851227","https://openalex.org/W4293088966","https://openalex.org/W2366868484","https://openalex.org/W2917463375","https://openalex.org/W2155219672","https://openalex.org/W2785906022"],"abstract_inverted_index":{"In":[0],"this":[1,98],"paper":[2],"we":[3],"address":[4],"a":[5,18,32,44,81,124],"min\u2013max":[6],"problem":[7],"of":[8,38,57],"fractional":[9],"quadratic":[10,28],"(not":[11,25],"necessarily":[12,26],"convex)":[13,27],"over":[14],"linear":[15,23],"functions":[16],"on":[17,35],"feasible":[19],"set":[20],"described":[21],"by":[22,114],"and":[24,70,80],"functions.":[29],"We":[30,105],"propose":[31],"conic":[33,47],"reformulation":[34],"the":[36,72,88,93,115,130],"cone":[37],"completely":[39],"positive":[40],"matrices.":[41],"By":[42],"relaxation,":[43],"doubly":[45],"nonnegative":[46],"formulation":[48],"is":[49,62,75,85],"used":[50],"to":[51,91,120],"provide":[52],"lower":[53,101,111],"bounds":[54,102,112],"with":[55],"evidence":[56,109],"very":[58],"small":[59],"gaps.":[60],"It":[61],"known":[63,126],"that":[64,110],"in":[65,77,87,128],"many":[66],"solvers":[67],"using":[68],"Branch":[69],"Bound":[71],"optimal":[73],"solution":[74],"obtained":[76],"early":[78],"stages":[79],"heavy":[82],"computational":[83],"price":[84],"paid":[86],"next":[89],"iterations":[90],"obtain":[92],"optimality":[94,131],"certificate.":[95,132],"To":[96],"reduce":[97],"effort":[99],"tight":[100],"are":[103,118],"crucial.":[104],"will":[106],"show":[107],"empirical":[108],"provided":[113],"copositive":[116],"relaxation":[117],"able":[119],"substantially":[121],"speed":[122],"up":[123],"well":[125],"solver":[127],"obtaining":[129]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}