{"id":"https://openalex.org/W4412192527","doi":"https://doi.org/10.1007/s12532-025-00285-z","title":"Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization","display_name":"Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization","publication_year":2025,"publication_date":"2025-07-11","ids":{"openalex":"https://openalex.org/W4412192527","doi":"https://doi.org/10.1007/s12532-025-00285-z"},"language":"en","primary_location":{"id":"doi:10.1007/s12532-025-00285-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00285-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00285-z.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"Mathematical Programming Computation","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/s12532-025-00285-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":["Faculty of Mathematics and Research Network Data Science, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-6288-9226","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Research Network Data Science, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029520397","display_name":"Bo Peng","orcid":"https://orcid.org/0000-0002-2650-0295"},"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":false,"raw_author_name":"Bo Peng","raw_affiliation_strings":["VGSCO, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2650-0295","affiliations":[{"raw_affiliation_string":"VGSCO, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027137324","display_name":"Yuzhou Qiu","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yuzhou Qiu","raw_affiliation_strings":["School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057209882","display_name":"E. Alper Y\u0131ld\u0131r\u0131m","orcid":"https://orcid.org/0000-0003-4141-3189"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Alper Y\u0131ld\u0131r\u0131m","raw_affiliation_strings":["School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK"],"raw_orcid":"https://orcid.org/0000-0003-4141-3189","affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023776719"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2390,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2390,"currency":"EUR","value_usd":3090},"fwci":1.075,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.74995157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"17","issue":"4","first_page":"617","last_page":"651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/theory-of-computation","display_name":"Theory of computation","score":0.7107337713241577},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.690472424030304},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5068617463111877},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4465918242931366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4423259496688843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4224976599216461},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3873363435268402},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3418266177177429},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2995164096355438},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07220691442489624}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7107337713241577},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.690472424030304},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5068617463111877},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4465918242931366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4423259496688843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4224976599216461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3873363435268402},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3418266177177429},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2995164096355438},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07220691442489624}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12532-025-00285-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00285-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00285-z.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"Mathematical Programming Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12532-025-00285-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00285-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00285-z.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"Mathematical Programming Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1957198323","display_name":"Tractable Convex Relaxations of Nonconvex Quadratic Optimization Problems","funder_award_id":"2445089","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4747624297","display_name":null,"funder_award_id":"W1260-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5803297947","display_name":"Maths DTP 2020 University of Edinburgh","funder_award_id":"EP/V520251/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7604315338","display_name":"Vienna Graduate School on Computational Optimization","funder_award_id":"W1260","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412192527.pdf","grobid_xml":"https://content.openalex.org/works/W4412192527.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W638016179","https://openalex.org/W1546734293","https://openalex.org/W1549791526","https://openalex.org/W1969120667","https://openalex.org/W1989288646","https://openalex.org/W2004304335","https://openalex.org/W2027470314","https://openalex.org/W2027574304","https://openalex.org/W2031130715","https://openalex.org/W2041781650","https://openalex.org/W2045513909","https://openalex.org/W2049967295","https://openalex.org/W2078600458","https://openalex.org/W2079135578","https://openalex.org/W2083137236","https://openalex.org/W2099030886","https://openalex.org/W2103765204","https://openalex.org/W2105630053","https://openalex.org/W2119667497","https://openalex.org/W2120575449","https://openalex.org/W2122983719","https://openalex.org/W2140320282","https://openalex.org/W2160625469","https://openalex.org/W2203301234","https://openalex.org/W2235959117","https://openalex.org/W2335862003","https://openalex.org/W2762341112","https://openalex.org/W2796071106","https://openalex.org/W2801961936","https://openalex.org/W2964012043","https://openalex.org/W3044264873","https://openalex.org/W3086620436","https://openalex.org/W3124804635","https://openalex.org/W4200630057","https://openalex.org/W4250915400","https://openalex.org/W4292175028","https://openalex.org/W4293423690","https://openalex.org/W4311230156","https://openalex.org/W4379162539","https://openalex.org/W4389994210","https://openalex.org/W4399401013","https://openalex.org/W4406775072","https://openalex.org/W6949689689"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W3036464408","https://openalex.org/W2020990755","https://openalex.org/W2377851227","https://openalex.org/W4293088966","https://openalex.org/W2366868484","https://openalex.org/W2102212721","https://openalex.org/W2917463375","https://openalex.org/W2155219672"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Standard":[2],"Quadratic":[3],"optimization":[4,15,129],"Problem":[5],"(StQP),":[6],"arguably":[7],"the":[8,28,105,119,158,164,186,190,208,212,218,221,226,235],"simplest":[9,24,32],"among":[10,59],"all":[11],"classes":[12],"of":[13,18,48,57,121,147,160,189,197,211,220,234],"NP-hard":[14,93],"problems,":[16],"consists":[17],"extremizing":[19],"a":[20,37,55,194],"quadratic":[21,205],"form":[22],"(the":[23,31],"nonlinear":[25],"polynomial)":[26],"over":[27,238],"standard":[29],"simplex":[30],"polytope/compact":[33],"feasible":[34],"set).":[35],"As":[36],"problem":[38,109,165,222],"class,":[39],"StQPs":[40,52,79,99],"may":[41],"be":[42],"nonconvex":[43],"with":[44,77,110,150,202],"an":[45,81,171],"exponential":[46],"number":[47,196],"inefficient":[49],"local":[50],"solutions.":[51],"arise":[53],"in":[54,68,116,118,193,200,232],"multitude":[56],"applications,":[58],"them":[60],"mathematical":[61],"finance,":[62],"machine":[63],"learning":[64],"(clustering),":[65],"and":[66,72],"modeling":[67],"biosciences":[69],"(e.g.,":[70],"selection":[71,108],"ecology).":[73],"This":[74],"paper":[75],"deals":[76],"such":[78,101],"under":[80,100],"additional":[82],"sparsity":[83,102],"or":[84],"cardinality":[85],"constraint,":[86],"which,":[87],"even":[88],"for":[89,136,157],"convex":[90,134],"objectives,":[91],"renders":[92],"problems.":[94],"One":[95],"motivation":[96],"to":[97,114,217],"study":[98],"restrictions":[103],"is":[104,155,214],"high-dimensional":[106],"portfolio":[107],"too":[111,178],"many":[112],"assets":[113],"handle,":[115],"particular,":[117,225],"presence":[120],"transaction":[122],"costs.":[123],"Here,":[124],"relying":[125],"on":[126],"modern":[127],"conic":[128],"techniques,":[130],"we":[131,169],"present":[132],"tractable":[133],"relaxations":[135,149,162,213],"this":[137],"relevant":[138],"but":[139],"difficult":[140],"problem.":[141],"We":[142],"propose":[143,170],"novel":[144],"equivalent":[145],"reformulations":[146],"these":[148,161],"significant":[151,195,230],"dimensional":[152],"reduction,":[153],"which":[154,175],"essential":[156],"tractability":[159],"when":[163],"size":[166],"grows.":[167],"Moreover,":[168],"instance":[172],"generation":[173],"procedure":[174],"systematically":[176],"avoids":[177],"easy":[179],"instances.":[180,198],"Our":[181],"extensive":[182],"computational":[183],"results":[184],"illustrate":[185],"high":[187],"quality":[188],"relaxation":[191],"bounds":[192],"Furthermore,":[199],"contrast":[201],"exact":[203],"mixed-integer":[204],"programming":[206],"models,":[207],"solution":[209,236],"time":[210,237],"very":[215],"robust":[216],"choices":[219],"parameters.":[223],"In":[224],"reduced":[227],"formulations":[228],"achieve":[229],"improvements":[231],"terms":[233],"their":[239],"counterparts.":[240]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}