{"id":"https://openalex.org/W4414425961","doi":"https://doi.org/10.48550/arxiv.2507.16648","title":"An unconditional lower bound for the active-set method in convex quadratic maximization","display_name":"An unconditional lower bound for the active-set method in convex quadratic maximization","publication_year":2025,"publication_date":"2025-07-22","ids":{"openalex":"https://openalex.org/W4414425961","doi":"https://doi.org/10.48550/arxiv.2507.16648"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.16648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.16648","pdf_url":"https://arxiv.org/pdf/2507.16648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.16648","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bach, Eleon","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bach, Eleon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021248592","display_name":"Yann Disser","orcid":"https://orcid.org/0000-0002-2085-0454"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Disser, Yann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034599189","display_name":"Sophie Huiberts","orcid":"https://orcid.org/0000-0003-2633-014X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huiberts, Sophie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036291098","display_name":"Nils Mosis","orcid":"https://orcid.org/0000-0002-0692-0647"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mosis, Nils","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9988999962806702,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6460999846458435},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5745999813079834},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5695000290870667},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5206999778747559},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.5042999982833862},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5012999773025513},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49900001287460327},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4846000075340271},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.47350001335144043},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4544999897480011}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8410999774932861},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6460999846458435},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5745999813079834},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5695000290870667},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5206999778747559},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.5042999982833862},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49900001287460327},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49720001220703125},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4544999897480011},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4433000087738037},{"id":"https://openalex.org/C205890394","wikidata":"https://www.wikidata.org/wiki/Q48297","display_name":"Parabola","level":2,"score":0.438400000333786},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3986999988555908},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36079999804496765},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31060001254081726},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C136719777","wikidata":"https://www.wikidata.org/wiki/Q3610230","display_name":"Logarithmically convex function","level":5,"score":0.2897000014781952},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2734000086784363},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2554999887943268},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2533999979496002},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.25220000743865967}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2507.16648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.16648","pdf_url":"https://arxiv.org/pdf/2507.16648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-05345258v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05345258","pdf_url":"https://hal.science/hal-05345258/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM-SIAM Symposium on Discrete Algorithms (SODA26), Jan 2026, Vancouver, Canada","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.2507.16648","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.16648","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.16648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.16648","pdf_url":"https://arxiv.org/pdf/2507.16648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,148],"prove":[1],"that":[2,130,153],"the":[3,13,27,35,71,91,96,155,160],"active-set":[4,92,156],"method":[5,93,98,157],"needs":[6,44],"an":[7],"exponential":[8],"number":[9],"of":[10,26,47,62,76,137,143,163,175],"iterations":[11],"in":[12,52],"worst-case":[14],"to":[15,22,55,158,173],"maximize":[16],"a":[17,56,59,78,100,109,117,134,138,150],"convex":[18,60],"quadratic":[19,151],"function":[20],"subject":[21],"linear":[23,88],"constraints,":[24],"regardless":[25],"pivot":[28,105],"rule":[29],"used.":[30],"This":[31],"substantially":[32],"improves":[33],"over":[34],"best":[36],"previously":[37],"known":[38],"lower":[39,101],"bound":[40,57,102],"[IPCO":[41,74],"2025],":[42],"which":[43],"objective":[45,152],"functions":[46],"polynomial":[48,61],"degrees":[49],"$\u03c9(\\log":[50],"d)$":[51],"dimension":[53],"$d$,":[54],"using":[58,123],"degree":[63,80],"2.":[64],"In":[65],"particular,":[66],"our":[67],"result":[68,113],"firmly":[69],"resolves":[70],"open":[72],"question":[73],"2025]":[75],"whether":[77],"constant":[79],"suffices,":[81],"and":[82,99],"it":[83,131],"represents":[84],"significant":[85],"progress":[86],"towards":[87],"objectives,":[89],"where":[90],"coincides":[94],"with":[95],"simplex":[97],"for":[103],"all":[104,142],"rules":[106],"would":[107],"constitute":[108],"major":[110],"breakthrough.":[111],"Our":[112],"is":[114,129],"based":[115],"on":[116],"novel":[118],"extended":[119],"formulation,":[120],"recursively":[121],"constructed":[122],"deformed":[124],"products.":[125],"Its":[126],"key":[127],"feature":[128],"projects":[132],"onto":[133],"polygonal":[135],"approximation":[136],"parabola":[139],"while":[140],"preserving":[141],"its":[144,176],"exponentially":[145],"many":[146],"vertices.":[147],"define":[149],"forces":[154],"follow":[159],"parabolic":[161],"boundary":[162],"this":[164],"projection,":[165],"without":[166],"allowing":[167],"any":[168],"shortcuts":[169],"along":[170],"chords":[171],"corresponding":[172],"edges":[174],"full-dimensional":[177],"preimage.":[178]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
