{"id":"https://openalex.org/W7213359149","doi":"https://doi.org/10.48550/arxiv.2609.13925","title":"Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints","display_name":"Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213359149","doi":"https://doi.org/10.48550/arxiv.2609.13925"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13925","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13925","pdf_url":"https://arxiv.org/pdf/2609.13925","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/2609.13925","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151847249","display_name":"Kang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Kang","raw_affiliation_strings":["School of Future Technology , Xi'an Jiaotong University , Xi'an , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Future Technology , Xi'an Jiaotong University , Xi'an , China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151773865","display_name":"Mengxiao Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Mengxiao","raw_affiliation_strings":["School of Automation Science and Engineering , Xi'an Jiaotong University , Xi'an , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation Science and Engineering , Xi'an Jiaotong University , Xi'an , China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151778496","display_name":"Siqi Xiong","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiong, Siqi","raw_affiliation_strings":["Department of Rehabilitation Sciences , The Hong Kong Polytechnic University , Hong Kong SAR , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Rehabilitation Sciences , The Hong Kong Polytechnic University , Hong Kong SAR , China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151768211","display_name":"Yi Xia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xia, Yi","raw_affiliation_strings":["School of Automation Science and Engineering , Xi'an Jiaotong University , Xi'an , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation Science and Engineering , Xi'an Jiaotong University , Xi'an , China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.711899995803833,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.711899995803833,"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":0.1005999967455864,"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"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0731000006198883,"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/convergence-analysis","display_name":"convergence analysis","score":0.5889999866485596},{"id":"https://openalex.org/keywords/karush-kuhn-tucker-conditions","display_name":"Karush-Kuhn-Tucker conditions","score":0.8650000095367432},{"id":"https://openalex.org/keywords/local-exponential-stability","display_name":"local exponential stability","score":0.550000011920929},{"id":"https://openalex.org/keywords/energy-analysis","display_name":"energy analysis","score":0.5170000195503235},{"id":"https://openalex.org/keywords/almost-sure-convergence","display_name":"almost sure convergence","score":0.6119999885559082},{"id":"https://openalex.org/keywords/nonlinear-constraints","display_name":"nonlinear constraints","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.771399974822998},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.6620000004768372},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5475999712944031},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5128999948501587},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5033000111579895},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4805000126361847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41929998993873596},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.37950000166893005},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3783999979496002},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.3605000078678131},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.35109999775886536},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.26739999651908875},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.26570001244544983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13925","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13925","pdf_url":"https://arxiv.org/pdf/2609.13925","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.2609.13925","doi":"https://doi.org/10.48550/arxiv.2609.13925","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13925","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:2609.13925","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13925","pdf_url":"https://arxiv.org/pdf/2609.13925","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/W7213359149.pdf","grobid_xml":"https://content.openalex.org/works/W7213359149.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1494085563","https://openalex.org/W2086929129","https://openalex.org/W2135779729","https://openalex.org/W2497446532","https://openalex.org/W2789265722","https://openalex.org/W2923772752","https://openalex.org/W2972448815","https://openalex.org/W3081147848","https://openalex.org/W3110749201","https://openalex.org/W4210417410","https://openalex.org/W4287114902","https://openalex.org/W4404500377","https://openalex.org/W4411235746"],"related_works":["https://openalex.org/W7168151839","https://openalex.org/W2923772752","https://openalex.org/W2152686991","https://openalex.org/W7203880158","https://openalex.org/W2026116392","https://openalex.org/W2034373500","https://openalex.org/W4391022099","https://openalex.org/W1976670711","https://openalex.org/W2341536965","https://openalex.org/W7093309515"],"abstract_inverted_index":{"This":[0],"work":[1],"studies":[2,139],"the":[3,29,32,47,76,92,106,131,141],"stability":[4],"and":[5,42,51,95,101,117,127,145,152],"convergence":[6,104,147],"of":[7,31,91,105,133],"augmented":[8,25,77],"primal-dual":[9,107],"dynamics":[10],"when":[11],"constraint":[12,19,69],"values":[13,70],"are":[14,71],"estimated":[15,72],"from":[16],"samples.":[17],"Unbiased":[18],"observations":[20],"can":[21],"produce":[22],"a":[23,40,53,57,85,110],"biased":[24],"multiplier":[26,78],"signal,":[27],"shifting":[28],"equilibria":[30,50],"mean":[33],"dynamics.":[34],"For":[35,80],"componentwise":[36],"inequalities,":[37],"we":[38],"give":[39],"necessary":[41],"sufficient":[43],"condition":[44],"for":[45],"preserving":[46],"Karush-Kuhn-Tucker":[48],"(KKT)":[49],"construct":[52],"convex":[54,82],"example":[55],"with":[56,148],"locally":[58],"exponentially":[59],"stable":[60],"equilibrium":[61,143],"that":[62],"violates":[63],"complementarity.":[64],"To":[65],"address":[66],"this":[67],"bias,":[68],"recursively":[73],"before":[74],"forming":[75],"signal.":[79],"smooth":[81],"conic":[83],"problems,":[84],"joint":[86],"energy":[87],"analysis":[88],"establishes":[89],"boundedness":[90],"primal,":[93],"dual,":[94],"estimation":[96,99],"states,":[97],"vanishing":[98],"error,":[100],"almost":[102],"sure":[103],"iterates":[108],"to":[109],"single":[111],"KKT":[112,150],"point":[113],"under":[114],"global":[115],"regularity":[116],"bounded":[118],"conditional":[119],"second":[120],"moments.":[121],"The":[122],"result":[123],"allows":[124],"nonunique":[125,149],"solutions":[126],"multipliers":[128],"while":[129],"keeping":[130],"number":[132],"samples":[134],"per":[135],"iteration":[136],"fixed.":[137],"Numerical":[138],"illustrate":[140],"predicted":[142],"bias":[144],"examine":[146],"points":[151],"nonlinear":[153],"constraints.":[154]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
