{"id":"https://openalex.org/W7220952997","doi":"https://doi.org/10.48550/arxiv.2610.09991","title":"Distances on Finite Constraint Systems and LICQ Radii in Nonlinear Programming","display_name":"Distances on Finite Constraint Systems and LICQ Radii in Nonlinear Programming","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220952997","doi":"https://doi.org/10.48550/arxiv.2610.09991"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09991","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09991","pdf_url":"https://arxiv.org/pdf/2610.09991","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/2610.09991","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018051479","display_name":"Kohei Hatano","orcid":"https://orcid.org/0000-0002-1536-1269","observed_orcids":["https://orcid.org/0000-0002-1536-1269"]},"institutions":[{"id":"https://openalex.org/I4210133125","display_name":"Mitsubishi Electric (Japan)","ror":"https://ror.org/033y26782","country_code":"JP","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hatano, Kohei","raw_affiliation_strings":["Information Technology R&D Center , Mitsubishi Electric Corporation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology R&D Center , Mitsubishi Electric Corporation","institution_ids":["https://openalex.org/I4210133125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018051479"],"corresponding_institution_ids":["https://openalex.org/I4210133125"],"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":0.6890000104904175,"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":0.6890000104904175,"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":0.30570000410079956,"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":0.0013000000035390258,"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/linear-independence-constraint-qualification","display_name":"linear independence constraint qualification","score":0.8220000267028809},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"nonlinear programming","score":0.8209999799728394},{"id":"https://openalex.org/keywords/karush-kuhn-tucker-conditions","display_name":"Karush-Kuhn-Tucker conditions","score":0.48399999737739563}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7272999882698059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6876000165939331},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6129000186920166},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5063999891281128},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4887999892234802},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4481000006198883},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.37290000915527344},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.34389999508857727},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.3167000114917755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30399999022483826},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C176783269","wikidata":"https://www.wikidata.org/wiki/Q5164378","display_name":"Constraint logic programming","level":4,"score":0.2655999958515167},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C79475747","wikidata":"https://www.wikidata.org/wiki/Q4913885","display_name":"Binary constraint","level":5,"score":0.25589999556541443}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09991","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09991","pdf_url":"https://arxiv.org/pdf/2610.09991","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.2610.09991","doi":"https://doi.org/10.48550/arxiv.2610.09991","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09991","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09991","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09991","pdf_url":"https://arxiv.org/pdf/2610.09991","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220952997.pdf","grobid_xml":"https://content.openalex.org/works/W7220952997.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2924136261","https://openalex.org/W3039256091","https://openalex.org/W4382797029","https://openalex.org/W4416179052"],"related_works":["https://openalex.org/W1967505494","https://openalex.org/W2388318005","https://openalex.org/W2932808730","https://openalex.org/W3158145877","https://openalex.org/W3014219249","https://openalex.org/W2580320326","https://openalex.org/W7098685999","https://openalex.org/W7096547607","https://openalex.org/W2147769470","https://openalex.org/W2075982138"],"abstract_inverted_index":{"Mathematical":[0],"programming":[1],"formulations":[2,127],"are":[3,56],"routinely":[4],"modified":[5],"through":[6],"algebraic":[7],"reformulations,":[8],"perturbations":[9],"of":[10,18,21,52,61,77,98,126,154],"constraint":[11,62],"functions,":[12],"and":[13,35,81,150],"the":[14,25,38,50,78,83,90,99,103,111,117,124,152],"addition":[15],"or":[16,159],"removal":[17],"constraints.":[19],"Some":[20],"these":[22],"modifications":[23],"preserve":[24],"feasible":[26,121,130],"set,":[27],"whereas":[28],"others":[29],"reflect":[30],"newly":[31],"imposed":[32],"modeling":[33],"requirements":[34],"therefore":[36],"change":[37],"optimization":[39],"problem":[40],"itself.":[41],"This":[42],"paper":[43],"develops":[44],"a":[45,87,95,120,132,156],"metric":[46],"framework":[47],"for":[48,147],"quantifying":[49],"robustness":[51],"formulation-dependent":[53],"properties.":[54],"Formulations":[55],"modeled":[57],"as":[58,116],"typed":[59],"collections":[60],"functions.":[63],"Within":[64],"each":[65],"fixed":[66],"typed-cardinality":[67],"class,":[68],"their":[69],"distance":[70,118],"is":[71],"defined":[72,115],"by":[73],"optimally":[74],"matching":[75],"constraints":[76],"same":[79],"type":[80],"measuring":[82],"resulting":[84],"discrepancies":[85],"in":[86],"norm":[88],"on":[89],"underlying":[91],"function":[92],"space.":[93],"As":[94],"concrete":[96],"demonstration":[97],"framework,":[100],"we":[101,142],"study":[102],"Linear":[104],"Independence":[105],"Constraint":[106],"Qualification":[107],"(LICQ).":[108],"We":[109],"introduce":[110],"pointwise":[112],"LICQ":[113,137],"radius,":[114],"from":[119],"formulation":[122],"to":[123],"set":[125],"that":[128],"remain":[129],"at":[131],"prescribed":[133],"point":[134],"but":[135],"fail":[136],"there.":[138],"Under":[139],"suitable":[140],"assumptions,":[141],"derive":[143],"an":[144],"explicit":[145],"formula":[146],"this":[148],"radius":[149],"characterize":[151],"effect":[153],"adding":[155],"single":[157],"equality":[158],"inequality":[160],"constraint.":[161]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}