{"id":"https://openalex.org/W2563569639","doi":"https://doi.org/10.1080/10556788.2016.1264397","title":"Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation","display_name":"Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation","publication_year":2016,"publication_date":"2016-12-13","ids":{"openalex":"https://openalex.org/W2563569639","doi":"https://doi.org/10.1080/10556788.2016.1264397","mag":"2563569639"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1264397","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1264397","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5073118424","display_name":"Pedro M. Castro","orcid":"https://orcid.org/0000-0002-4898-8922"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I7883018","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","ror":"https://ror.org/00snfqn58","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210146676","https://openalex.org/I7883018"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Pedro M. Castro","raw_affiliation_strings":["Centro de Matem\u00e1tica Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional, Faculdade de Ci\u00eancias, Universidade de Lisboa, Lisboa 1749-016, Portugal"],"raw_orcid":"https://orcid.org/0000-0002-4898-8922","affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional, Faculdade de Ci\u00eancias, Universidade de Lisboa, Lisboa 1749-016, Portugal","institution_ids":["https://openalex.org/I7883018","https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073118424"],"corresponding_institution_ids":["https://openalex.org/I141596103","https://openalex.org/I7883018"],"apc_list":null,"apc_paid":null,"fwci":2.3024,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88029725,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"32","issue":"4","first_page":"719","last_page":"737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9818000197410583,"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":0.7552275061607361},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.5567471981048584},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5419548153877258},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5346208214759827},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5009560585021973},{"id":"https://openalex.org/keywords/branch-and-cut","display_name":"Branch and cut","score":0.48545128107070923},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4697181284427643},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.4633771479129791},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4433518648147583},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.44242382049560547},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4374712109565735},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.42783647775650024},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.42381757497787476},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42062586545944214},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.41217750310897827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3966381549835205},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.32204920053482056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18081048130989075}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7552275061607361},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.5567471981048584},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5419548153877258},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5346208214759827},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5009560585021973},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.48545128107070923},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4697181284427643},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.4633771479129791},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4433518648147583},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.44242382049560547},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4374712109565735},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42783647775650024},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.42381757497787476},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42062586545944214},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.41217750310897827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3966381549835205},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.32204920053482056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18081048130989075},{"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2016.1264397","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1264397","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G7573641107","display_name":null,"funder_award_id":"UID/MAT/04561/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W114465074","https://openalex.org/W986230988","https://openalex.org/W1966205829","https://openalex.org/W1967871541","https://openalex.org/W1971583973","https://openalex.org/W1972997295","https://openalex.org/W1975167632","https://openalex.org/W1986668990","https://openalex.org/W1987429668","https://openalex.org/W1988622494","https://openalex.org/W1999917117","https://openalex.org/W2001741445","https://openalex.org/W2004407575","https://openalex.org/W2007520715","https://openalex.org/W2007967264","https://openalex.org/W2009015381","https://openalex.org/W2011970986","https://openalex.org/W2014328192","https://openalex.org/W2020500787","https://openalex.org/W2021674665","https://openalex.org/W2021996638","https://openalex.org/W2026964350","https://openalex.org/W2027627501","https://openalex.org/W2035132227","https://openalex.org/W2037054598","https://openalex.org/W2045982444","https://openalex.org/W2048866292","https://openalex.org/W2050339136","https://openalex.org/W2065849120","https://openalex.org/W2068965055","https://openalex.org/W2070105389","https://openalex.org/W2071334094","https://openalex.org/W2075740111","https://openalex.org/W2079967559","https://openalex.org/W2081929325","https://openalex.org/W2086532413","https://openalex.org/W2128562811","https://openalex.org/W2133160914","https://openalex.org/W2140871507","https://openalex.org/W2149454052","https://openalex.org/W2150023190","https://openalex.org/W2218007488","https://openalex.org/W2237869155","https://openalex.org/W2306380836","https://openalex.org/W2315353851","https://openalex.org/W2335572701"],"related_works":["https://openalex.org/W2087596644","https://openalex.org/W58208513","https://openalex.org/W1862675270","https://openalex.org/W4235176699","https://openalex.org/W2009127293","https://openalex.org/W2158520126","https://openalex.org/W2994371406","https://openalex.org/W2364907623","https://openalex.org/W2037211437","https://openalex.org/W1242960107"],"abstract_inverted_index":{"Spatial":[0],"branch-and-bound":[1],"(B&B)":[2],"is":[3,112,152],"widely":[4],"used":[5],"for":[6,41,54,102],"the":[7,19,22,35,79,83,89,116,129,133,140,149,155],"global":[8,36,157],"optimization":[9,158],"of":[10,21,59,85,91,115,128,135,142,145,165],"non-convex":[11],"problems.":[12,108],"It":[13],"basically":[14],"works":[15],"by":[16],"iteratively":[17],"reducing":[18],"domain":[20],"variables":[23,87],"so":[24,118],"that":[25,31,50,154],"tighter":[26],"relaxations":[27],"can":[28,51,160],"be":[29],"achieved":[30],"ultimately":[32],"converge":[33],"to":[34,78,96,120,137,163,173],"optimal":[37],"solution.":[38],"Recent":[39],"developments":[40],"bilinear":[42],"problems":[43,147],"have":[44],"brought":[45],"us":[46],"piecewise":[47],"relaxation":[48],"techniques":[49],"prove":[52],"optimality":[53,169],"a":[55,74,143],"sufficiently":[56],"large":[57],"number":[58,84,90,134],"partitions":[60],"and":[61,131,177],"hence":[62],"avoid":[63],"spatial":[64,100],"B&B":[65,101],"altogether.":[66],"Of":[67],"these,":[68],"normalized":[69],"multiparametric":[70],"disaggregation":[71],"(NMDT)":[72],"exhibits":[73],"good":[75],"performance":[76],"due":[77],"logarithmic":[80],"increase":[81],"in":[82,125,168],"binary":[86],"with":[88,99],"partitions.":[92],"We":[93],"now":[94],"propose":[95],"integrate":[97],"NMDT":[98],"solving":[103],"mixed-integer":[104],"quadratically":[105],"constrained":[106],"minimization":[107],"Optimality-based":[109],"bound":[110],"tightening":[111],"also":[113],"part":[114],"algorithm":[117,159],"as":[119],"compute":[121],"tight":[122],"lower":[123],"bounds":[124],"every":[126],"step":[127],"search":[130],"reduce":[132],"nodes":[136],"explore.":[138],"Through":[139],"solution":[141],"set":[144],"benchmark":[146],"from":[148],"literature,":[150],"it":[151],"shown":[153],"new":[156],"potentially":[161],"lead":[162],"orders":[164],"magnitude":[166],"reduction":[167],"gap":[170],"when":[171],"compared":[172],"commercial":[174],"solvers":[175],"BARON":[176],"GloMIQO.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}