{"id":"https://openalex.org/W7223290261","doi":"https://doi.org/10.48550/arxiv.2610.30300","title":"Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions","display_name":"Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223290261","doi":"https://doi.org/10.48550/arxiv.2610.30300"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30300","pdf_url":"https://arxiv.org/pdf/2610.30300","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/2610.30300","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025869838","display_name":"Gabriel P. Langlois","orcid":"https://orcid.org/0000-0002-1845-9536","observed_orcids":["https://orcid.org/0000-0002-1845-9536"]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Langlois, Gabriel P.","raw_affiliation_strings":["Department of Mathematics , University of Illinois Urbana-Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Illinois Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039702204","display_name":"Akwum Onwunta","orcid":"https://orcid.org/0000-0003-2110-8881","observed_orcids":["https://orcid.org/0000-0003-2110-8881"]},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Onwunta, Akwum","raw_affiliation_strings":["Industrial and Systems Engineering , Lehigh University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial and Systems Engineering , Lehigh University","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076546851","display_name":"J\u00e9r\u00f4me Darbon","orcid":"https://orcid.org/0000-0003-0483-7919","observed_orcids":["https://orcid.org/0000-0003-0483-7919"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darbon, J\u00e9r\u00f4me","raw_affiliation_strings":["Division of Applied Mathematics , Brown University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics , Brown University","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.9179999828338623,"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":0.9179999828338623,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.07029999792575836,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.002199999988079071,"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-programming","display_name":"linear programming","score":0.5239999890327454},{"id":"https://openalex.org/keywords/differential-inclusions","display_name":"differential inclusions","score":0.9729999899864197},{"id":"https://openalex.org/keywords/non-negative-least-squares","display_name":"non-negative least squares","score":0.7910000085830688},{"id":"https://openalex.org/keywords/positivity-preserving-limiter","display_name":"positivity-preserving limiter","score":0.7429999709129333},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"discontinuous Galerkin method","score":0.8320000171661377},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8759999871253967},{"id":"https://openalex.org/keywords/poisson-equation","display_name":"Poisson equation","score":0.9570000171661377},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.8790000081062317},{"id":"https://openalex.org/keywords/douglas-rachford-splitting","display_name":"Douglas-Rachford splitting","score":0.9010000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7698000073432922},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.6362000107765198},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4569000005722046},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.45680001378059387},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4544000029563904},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4397999942302704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.414000004529953},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.3736000061035156},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3625999987125397},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35530000925064087},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3483999967575073},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.3061000108718872},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.29660001397132874},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.2906000018119812},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30300","pdf_url":"https://arxiv.org/pdf/2610.30300","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.2610.30300","doi":"https://doi.org/10.48550/arxiv.2610.30300","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30300","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:2610.30300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30300","pdf_url":"https://arxiv.org/pdf/2610.30300","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/W7223290261.pdf","grobid_xml":"https://content.openalex.org/works/W7223290261.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2026993378","https://openalex.org/W2268206128","https://openalex.org/W4399365340","https://openalex.org/W4402639078","https://openalex.org/W4410480199","https://openalex.org/W4411970695","https://openalex.org/W4415844791","https://openalex.org/W4415946692","https://openalex.org/W4417070144","https://openalex.org/W7095002396"],"related_works":["https://openalex.org/W2039552580","https://openalex.org/W1250836021","https://openalex.org/W2162196200","https://openalex.org/W1906964498","https://openalex.org/W2121738381","https://openalex.org/W3215464813","https://openalex.org/W2170197658","https://openalex.org/W229779984","https://openalex.org/W48979750","https://openalex.org/W1207170590"],"abstract_inverted_index":{"Linear":[0],"and":[1,57,60,132,137,169,186,194,229,236],"convex":[2,156],"quadratic":[3,157],"programs":[4,19,136],"are":[5],"fundamental":[6],"problems":[7,190],"in":[8,20,38,51,232],"optimization.":[9],"While":[10],"many":[11,95,130],"methods":[12],"have":[13,27],"been":[14],"developed":[15],"for":[16,79,154,181,191],"solving":[17],"these":[18,66],"large-scale":[21],"applications,":[22],"to":[23,29,119,134,162,177,187,226],"our":[24],"knowledge":[25],"none":[26],"attempted":[28],"solve":[30,69],"their":[31],"continuous-time":[32],"gradient":[33,49,90,152],"flow,":[34],"a":[35,112,178,182],"differential":[36,81],"inclusion,":[37],"full":[39],"generality":[40],"without":[41],"assumptions":[42],"beyond":[43],"feasibility.":[44],"Recent":[45],"work":[46],"solved":[47],"the":[48,58,70,75,86,89,151,192,198,200,204,210,216,223],"flows":[50],"two":[52,120],"special":[53],"cases,":[54],"basis":[55],"pursuit":[56],"lasso,":[59],"obtained":[61,98],"competitive":[62,231],"algorithms.":[63,121],"Motivated":[64],"by":[65],"results,":[67],"we":[68,83,145],"general":[71,155],"case":[72],"exactly.":[73],"Using":[74],"minimal":[76,147,219],"selection":[77,148,220],"principle":[78],"monotone":[80],"inclusions,":[82],"show":[84],"that":[85],"trajectory":[87],"of":[88,93,114],"flow":[91,153],"consists":[92],"finitely":[94,129],"pieces,":[96],"each":[97],"from":[99],"one":[100,167],"nonnegative":[101],"least-squares":[102],"problem.":[103],"Its":[104,159],"final":[105],"piece":[106],"yields":[107],"an":[108,163],"optimal":[109,164,188,224],"solution":[110,165],"or":[111],"certificate":[113],"unboundedness.":[115,172],"This":[116],"analysis":[117],"leads":[118],"The":[122,141],"first":[123,201],"algorithm":[124,202],"is":[125,230],"exact,":[126],"terminates":[127],"after":[128],"steps,":[131],"applies":[133],"linear":[135],"projections":[138],"onto":[139],"polyhedra.":[140],"second":[142],"algorithm,":[143],"which":[144],"call":[146],"descent,":[149],"discretizes":[150],"programs.":[158],"iterates":[160],"converge":[161],"when":[166],"exists":[168],"otherwise":[170],"certify":[171],"We":[173],"apply":[174],"both":[175],"algorithms":[176],"positivity-preserving":[179],"limiter":[180],"discontinuous":[183],"Galerkin":[184],"scheme":[185],"control":[189,217],"Poisson":[193],"heat":[195],"equations.":[196],"In":[197],"limiter,":[199],"conserves":[203],"total":[205],"mass":[206],"more":[207],"accurately":[208],"than":[209],"state-of-the-art":[211],"Douglas--Rachford":[212],"splitting":[213],"method.":[214],"On":[215],"problems,":[218],"descent":[221],"reaches":[222],"value":[225],"machine":[227],"precision":[228],"time":[233],"with":[234],"commercial":[235],"open-source":[237],"solvers.":[238]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}