{"id":"https://openalex.org/W7204967744","doi":"https://doi.org/10.48550/arxiv.2608.30933","title":"Goldfarb-Idnani Revisited:Invariants, Certificates, and the Limits of Guessing","display_name":"Goldfarb-Idnani Revisited:Invariants, Certificates, and the Limits of Guessing","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204967744","doi":"https://doi.org/10.48550/arxiv.2608.30933"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30933","pdf_url":"https://arxiv.org/pdf/2608.30933","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30933","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052308379","display_name":"Thomas Schmelzer","orcid":"https://orcid.org/0009-0009-9771-3501","observed_orcids":["https://orcid.org/0009-0009-9771-3501"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmelzer, Thomas","raw_affiliation_strings":["Jebel Quant Research , Abu Dhabi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jebel Quant Research , Abu Dhabi","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5140678665","display_name":"Martin Stoll","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stoll, Martin","raw_affiliation_strings":["Faculty of Mathematics , TU Chemnitz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , TU Chemnitz , Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.9984999895095825,"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":0.9984999895095825,"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":0.000699999975040555,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/active-set-method","display_name":"active set method","score":0.6919999718666077},{"id":"https://openalex.org/keywords/bound-constraints","display_name":"bound constraints","score":0.46299999952316284},{"id":"https://openalex.org/keywords/inequality-constraints","display_name":"inequality constraints","score":0.7509999871253967},{"id":"https://openalex.org/keywords/karush-kuhn-tucker-conditions","display_name":"Karush-Kuhn-Tucker conditions","score":0.6970000267028809},{"id":"https://openalex.org/keywords/finite-termination","display_name":"finite termination","score":0.6019999980926514}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.6553000211715698},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6370000243186951},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6261000037193298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6090999841690063},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5260999798774719},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C68767595","wikidata":"https://www.wikidata.org/wiki/Q1677999","display_name":"Contiguity","level":2,"score":0.35179999470710754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33390000462532043},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31520000100135803},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.29019999504089355},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2791999876499176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27410000562667847},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.27000001072883606},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C109271563","wikidata":"https://www.wikidata.org/wiki/Q7451830","display_name":"Separation property","level":5,"score":0.25600001215934753},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2515999972820282},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30933","pdf_url":"https://arxiv.org/pdf/2608.30933","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2608.30933","doi":"https://doi.org/10.48550/arxiv.2608.30933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30933","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30933","pdf_url":"https://arxiv.org/pdf/2608.30933","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204967744.pdf","grobid_xml":"https://content.openalex.org/works/W7204967744.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7204191616"],"related_works":["https://openalex.org/W2242761019","https://openalex.org/W875426949","https://openalex.org/W7096033082","https://openalex.org/W7100835319","https://openalex.org/W4226183239","https://openalex.org/W2216549247","https://openalex.org/W2519387373","https://openalex.org/W2545770483","https://openalex.org/W7118870014","https://openalex.org/W3153176788"],"abstract_inverted_index":{"The":[0,59,97,121],"dual":[1],"active-set":[2],"method":[3,137],"of":[4,70,75,115,163,187],"Goldfarb":[5],"and":[6,16,30,46,126],"Idnani":[7],"solves":[8],"the":[9,35,55,76,116,119,127,131,136,182],"strictly":[10],"convex":[11],"quadratic":[12],"program":[13],"by":[14],"adding":[15],"dropping":[17,170],"one":[18],"constraint":[19,154],"at":[20,44],"a":[21,63,67,113],"time,":[22],"requiring":[23],"no":[24],"phase":[25],"one.":[26],"Primal--dual":[27],"active":[28,42,183],"set":[29,43,65,184],"block":[31],"principal":[32,68],"pivoting":[33],"skip":[34],"walk":[36],"altogether:":[37],"they":[38],"guess":[39,56],"an":[40],"entire":[41],"once":[45],"repair":[47],"it":[48],"from":[49,173],"returning":[50],"signs.":[51],"For":[52,84],"bound":[53],"constraints":[54],"is":[57,66,93,100,124],"safe.":[58],"system":[60,99],"solved":[61],"on":[62],"candidate":[64,142],"submatrix":[69],"$G^{-1}$,":[71],"positive":[72,104],"definite":[73,105],"regardless":[74],"guess;":[77],"this":[78,156],"$P$-matrix":[79,122],"property":[80,114,123],"guarantees":[81],"finite":[82],"termination.":[83],"$C^\\top":[85],"x":[86],"\\ge":[87],"b$":[88],"that":[89],"hypothesis":[90],"fails,":[91],"which":[92],"our":[94],"central":[95],"focus.":[96],"working-set":[98],"$C_{\\mathcal{A}}^\\top":[101],"G^{-1}":[102],"C_{\\mathcal{A}}$,":[103],"only":[106],"when":[107],"$C_{\\mathcal{A}}$":[108],"has":[109],"full":[110],"column":[111],"rank,":[112],"guess,":[117],"not":[118],"data.":[120],"lost":[125],"structural":[128],"obstruction":[129],"invalidates":[130],"guarantee.":[132],"Strict":[133],"convexity":[134],"keeps":[135],"usable:":[138],"KKT":[139],"conditions":[140],"make":[141],"sets":[143],"certified":[144,171],"rather":[145],"than":[146],"trusted.":[147],"Over":[148],"600":[149],"random":[150],"instances":[151],"across":[152],"four":[153],"families":[155],"failure":[157,166],"never":[158],"occurs.":[159],"However,":[160],"duplicating":[161],"columns":[162],"$C$":[164],"raises":[165],"rates":[167],"to":[168,175],"93\\%,":[169],"fraction":[172],"100\\%":[174],"zero.":[176],"On":[177],"real":[178],"long-only":[179],"portfolio":[180],"data,":[181],"reaches":[185],"442":[186],"$494":[188],"+":[189],"1$":[190],"constraints.":[191]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}