{"id":"https://openalex.org/W7214404265","doi":"https://doi.org/10.48550/arxiv.2609.29888","title":"Randomized Branch Methods with Inexact Subproblems for Bouligand Stationarity in Linear and Quadratic Programs with Complementarity Constraints","display_name":"Randomized Branch Methods with Inexact Subproblems for Bouligand Stationarity in Linear and Quadratic Programs with Complementarity Constraints","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214404265","doi":"https://doi.org/10.48550/arxiv.2609.29888"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29888","pdf_url":"https://arxiv.org/pdf/2609.29888","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045158222","display_name":"Ziyin Hu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu, Ziyin","raw_affiliation_strings":["Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152824360","display_name":"Xin Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Xin","raw_affiliation_strings":["Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152864307","display_name":"Shangzhi Zeng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Shangzhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152785636","display_name":"Jin Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Jin","raw_affiliation_strings":["Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Southern University of Science and Technology , Shenzhen 518055 , People's Republic of China","institution_ids":["https://openalex.org/I3045169105"]}]}],"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":0.8529999852180481,"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":0.8529999852180481,"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":0.14100000262260437,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0008999999845400453,"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/bi-level-optimization","display_name":"bi-level optimization","score":0.5580000281333923},{"id":"https://openalex.org/keywords/finite-termination","display_name":"finite termination","score":0.44999998807907104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7409999966621399},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6107000112533569},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.546999990940094},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5386999845504761},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.4562999904155731},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4530999958515167},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.4474000036716461},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33550000190734863},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31859999895095825},{"id":"https://openalex.org/C2333172","wikidata":"https://www.wikidata.org/wiki/Q1425985","display_name":"Preorder","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.28999999165534973},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.2757999897003174},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29888","pdf_url":"https://arxiv.org/pdf/2609.29888","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.2609.29888","doi":"https://doi.org/10.48550/arxiv.2609.29888","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29888","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:2609.29888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29888","pdf_url":"https://arxiv.org/pdf/2609.29888","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":[{"id":"https://openalex.org/G2035519848","display_name":null,"funder_award_id":"20250530150024003","funder_id":"https://openalex.org/F4320329791","funder_display_name":"Shenzhen Fundamental Research Program"},{"id":"https://openalex.org/G335111166","display_name":null,"funder_award_id":"12125108","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4019248187","display_name":null,"funder_award_id":"12501429","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8533620077","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327605","display_name":"Southern University of Science and Technology","ror":null},{"id":"https://openalex.org/F4320329791","display_name":"Shenzhen Fundamental Research Program","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214404265.pdf","grobid_xml":"https://content.openalex.org/works/W7214404265.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3090783725","https://openalex.org/W2041272264","https://openalex.org/W2057012359","https://openalex.org/W1976886395","https://openalex.org/W2962818638","https://openalex.org/W2091988699","https://openalex.org/W1995138983","https://openalex.org/W2051515327","https://openalex.org/W7097811869","https://openalex.org/W2148239522"],"abstract_inverted_index":{"We":[0],"develop":[1],"randomized":[2],"branch":[3,82],"methods":[4,27,114,173],"for":[5,38],"finding":[6],"Bouligand-stationary":[7],"(B-stationary)":[8],"points":[9,122,175],"of":[10,32,139],"linear":[11,23],"and":[12,19,36,97,135,157,180],"quadratic":[13,80,83,155],"programs":[14,84],"with":[15,78,165,176],"complementarity":[16,184],"constraints":[17],"(LPCCs":[18],"QPCCs)":[20],"using":[21],"only":[22,104],"programming":[24],"subproblems.":[25],"The":[26],"exploit":[28],"the":[29,33,68,109,112,126,172],"finite-union":[30],"geometry":[31],"feasible":[34],"set":[35],"search":[37],"first-order":[39],"descent":[40],"on":[41,148,182],"randomly":[42],"selected":[43],"compatible":[44],"branches.":[45],"For":[46,74,125],"LPCCs,":[47],"an":[48,56,62,140],"exact":[49],"method":[50,59],"optimizes":[51],"over":[52],"sampled":[53,69],"branches,":[54],"while":[55],"inexact":[57],"simplex":[58],"can":[60],"accept":[61],"improving":[63],"branch-feasible":[64],"vertex":[65],"before":[66],"solving":[67],"penalty":[70],"problem":[71],"to":[72],"optimality.":[73],"QPCCs,":[75],"including":[76],"problems":[77],"indefinite":[79],"objectives,":[81],"are":[85],"replaced":[86],"by":[87],"linearized":[88],"trust-region":[89],"subproblems;":[90],"a":[91,132],"ratio":[92],"test":[93],"ensures":[94],"actual":[95],"decrease,":[96],"thresholded":[98],"sampling":[99],"detects":[100],"branches":[101],"that":[102,171],"emerge":[103],"at":[105,120],"accumulation":[106,137],"points.":[107],"Under":[108],"stated":[110],"assumptions,":[111],"LPCC":[113],"stabilize":[115],"after":[116],"finitely":[117],"many":[118],"changes":[119],"B-stationary":[121,133,144],"almost":[123,145],"surely.":[124,146],"QPCC":[127],"method,":[128],"finite":[129],"termination":[130],"yields":[131],"point,":[134],"every":[136],"point":[138],"infinite":[141],"run":[142],"is":[143],"Experiments":[147],"bilevel-induced":[149],"instances,":[150,163],"instances":[151],"arising":[152],"from":[153],"inverse":[154],"programming,":[156],"sparse":[158],"affine":[159],"generalized":[160],"Nash":[161],"equilibrium":[162],"together":[164],"129":[166],"MacMPEC":[167],"embedding":[168],"tests,":[169],"show":[170],"return":[174],"competitive":[177],"objective":[178],"quality":[179],"runtimes":[181],"large-scale":[183],"systems.":[185]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-26T00:00:00"}
