{"id":"https://openalex.org/W7223068249","doi":"https://doi.org/10.48550/arxiv.2610.26504","title":"On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport","display_name":"On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223068249","doi":"https://doi.org/10.48550/arxiv.2610.26504"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26504","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26504","pdf_url":"https://arxiv.org/pdf/2610.26504","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/2610.26504","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132885829","display_name":"Giorgia Bifronte","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bifronte, Giorgia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058720571","display_name":"Armand Ley","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ley, Armand","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039149127","display_name":"Maxime Sylvestre","orcid":"https://orcid.org/0009-0004-4033-5048","observed_orcids":["https://orcid.org/0009-0004-4033-5048"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sylvestre, Maxime","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9301999807357788,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9301999807357788,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.010300000198185444,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.008899999782443047,"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/linear-convergence","display_name":"linear convergence","score":0.7670000195503235},{"id":"https://openalex.org/keywords/sinkhorn-algorithm","display_name":"Sinkhorn algorithm","score":0.7689999938011169},{"id":"https://openalex.org/keywords/block-coordinate-ascent","display_name":"block coordinate ascent","score":0.8550000190734863},{"id":"https://openalex.org/keywords/polyak-ojasiewicz-inequality","display_name":"Polyak-\u0141ojasiewicz inequality","score":0.8970000147819519},{"id":"https://openalex.org/keywords/coercivity-estimates","display_name":"coercivity estimates","score":0.6840000152587891},{"id":"https://openalex.org/keywords/l-infinity-bounds","display_name":"L-infinity bounds","score":0.7760000228881836},{"id":"https://openalex.org/keywords/strong-convexity","display_name":"strong convexity","score":0.8849999904632568},{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8650000095367432},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6269999742507935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6007999777793884},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4925000071525574},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4375},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3779999911785126},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.3734999895095825},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.35269999504089355},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.337799996137619},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3181000053882599},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3086000084877014},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.275299996137619},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26504","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26504","pdf_url":"https://arxiv.org/pdf/2610.26504","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.2610.26504","doi":"https://doi.org/10.48550/arxiv.2610.26504","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26504","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:2610.26504","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26504","pdf_url":"https://arxiv.org/pdf/2610.26504","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/W7223068249.pdf","grobid_xml":"https://content.openalex.org/works/W7223068249.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2907619282","https://openalex.org/W4387928542","https://openalex.org/W4390810522","https://openalex.org/W4415249815","https://openalex.org/W7160900955"],"related_works":["https://openalex.org/W7213563852","https://openalex.org/W7129091806","https://openalex.org/W4287258465","https://openalex.org/W4410192895","https://openalex.org/W7167144900","https://openalex.org/W4364385668","https://openalex.org/W4392678168","https://openalex.org/W2907619282","https://openalex.org/W4411911684","https://openalex.org/W4387928542"],"abstract_inverted_index":{"We":[0,128],"prove":[1],"a":[2,7,21,71,115,124],"linear":[3,58,125],"convergence":[4,59,126,138],"rate":[5],"of":[6,60,78,140],"Sinkhorn-type":[8],"algorithm":[9,19],"for":[10,29,38,87],"entropic":[11],"martingale":[12,44,89],"optimal":[13],"transport":[14],"in":[15],"arbitrary":[16],"dimension.":[17],"The":[18],"follows":[20],"block-coordinate":[22],"ascent":[23],"scheme,":[24],"alternating":[25],"exact":[26],"Sinkhorn":[27],"updates":[28],"the":[30,39,43,52,61,76,79,85,88,101,120,137,141],"marginal":[31],"potentials":[32],"with":[33,42,82,106,133],"an":[34],"explicit":[35],"gradient":[36,77],"step":[37],"potential":[40,86],"associated":[41],"constraint.":[45,90],"Under":[46],"irreducibility":[47],"and":[48,65,108],"non-degeneracy":[49],"assumptions":[50],"on":[51,70,100],"compactly":[53],"supported":[54],"marginals,":[55],"we":[56],"establish":[57,96],"dual":[62,80],"objective":[63],"values":[64],"iterates.":[66,102],"Our":[67],"analysis":[68],"relies":[69],"pointwise":[72],"coercivity":[73],"estimate":[74],"involving":[75],"functional":[81],"respect":[83],"to":[84,95],"This":[91],"property":[92],"allows":[93],"us":[94],"uniform":[97,116],"$L^{\\infty}$":[98],"bounds":[99,105],"Combining":[103],"these":[104],"smoothness":[107],"strong":[109],"convexity":[110],"modulo":[111],"affine":[112],"invariances":[113],"yields":[114],"Polyak--\u0141ojasiewicz":[117],"inequality":[118],"along":[119],"iterations":[121],"and,":[122],"consequently,":[123],"rate.":[127],"complement":[129],"our":[130],"theoretical":[131],"results":[132],"numerical":[134],"experiments":[135],"illustrating":[136],"behavior":[139],"algorithm.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}