{"id":"https://openalex.org/W7211890002","doi":"https://doi.org/10.48550/arxiv.2609.05062","title":"From plans to maps: Nonlocal regularization of optimal transport","display_name":"From plans to maps: Nonlocal regularization of optimal transport","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211890002","doi":"https://doi.org/10.48550/arxiv.2609.05062"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05062","pdf_url":"https://arxiv.org/pdf/2609.05062","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":"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/2609.05062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120057111","display_name":"Marcello Carioni","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Carioni, Marcello","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093271776","display_name":"Leonardo Del Grande","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Del Grande, Leonardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122777701","display_name":"Jos\u00e9 A. Iglesias","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Iglesias, Jos\u00e9 A.","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041018843","display_name":"Hidde Sch\u00f6nberger","orcid":"https://orcid.org/0000-0001-5140-5508","observed_orcids":["https://orcid.org/0000-0001-5140-5508"]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sch\u00f6nberger, Hidde","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , 7500AE Enschede , The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]}],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9990000128746033,"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":0.9990000128746033,"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/T10545","display_name":"Optimization and Variational Analysis","score":9.999999747378752e-05,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.9869999885559082},{"id":"https://openalex.org/keywords/nonlocal-regularization","display_name":"nonlocal regularization","score":0.9860000014305115},{"id":"https://openalex.org/keywords/monge-kantorovich-problem","display_name":"Monge-Kantorovich problem","score":0.7279999852180481},{"id":"https://openalex.org/keywords/transport-plans","display_name":"transport plans","score":0.5529999732971191},{"id":"https://openalex.org/keywords/interaction-kernel","display_name":"interaction kernel","score":0.4320000112056732},{"id":"https://openalex.org/keywords/gamma-convergence","display_name":"Gamma-convergence","score":0.8100000023841858},{"id":"https://openalex.org/keywords/first-order-optimality-conditions","display_name":"first-order optimality conditions","score":0.8510000109672546},{"id":"https://openalex.org/keywords/mass-splitting","display_name":"mass splitting","score":0.6700000166893005},{"id":"https://openalex.org/keywords/singular-kernels","display_name":"singular kernels","score":0.38199999928474426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7649999856948853},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.652899980545044},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5414999723434448},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4650000035762787},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39079999923706055},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2822999954223633},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.26440000534057617}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05062","pdf_url":"https://arxiv.org/pdf/2609.05062","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.05062","doi":"https://doi.org/10.48550/arxiv.2609.05062","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05062","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:2609.05062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05062","pdf_url":"https://arxiv.org/pdf/2609.05062","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G522777052","display_name":null,"funder_award_id":"F.6002.25","funder_id":"https://openalex.org/F4320321390","funder_display_name":"Fonds De La Recherche Scientifique - FNRS"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211890002.pdf","grobid_xml":"https://content.openalex.org/works/W7211890002.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3039389963","https://openalex.org/W4414839321"],"related_works":["https://openalex.org/W2263839075","https://openalex.org/W4389098073","https://openalex.org/W3093482044","https://openalex.org/W2918963622","https://openalex.org/W3155924879","https://openalex.org/W2986201115","https://openalex.org/W4386081812","https://openalex.org/W7100477860","https://openalex.org/W7169829730","https://openalex.org/W2963671455"],"abstract_inverted_index":{"We":[0,26,79],"introduce":[1],"a":[2,40,58,120,126,131,148,159],"nonlocal":[3,111],"regularization":[4,15],"of":[5,74,143,154],"optimal":[6],"transport":[7,35,144],"that":[8,62],"bridges":[9],"Kantorovich":[10,47,96],"and":[11,48,76,84,124,157],"Monge":[12,49,107],"formulations.":[13],"The":[14,89],"penalizes":[16],"oscillations":[17],"through":[18],"an":[19],"interaction":[20],"kernel":[21],"singular":[22],"near":[23],"the":[24,45,54,86,94,99,138,141,152,164],"diagonal.":[25],"show":[27],"that,":[28],"for":[29,71],"sufficiently":[30],"strong":[31],"singularities,":[32],"every":[33],"finite-energy":[34,106],"plan":[36],"is":[37],"induced":[38],"by":[39],"map,":[41],"yielding":[42],"equivalence":[43],"between":[44],"regularized":[46,90],"problems.":[50],"For":[51],"fractional":[52,59],"kernels,":[53],"regularizer":[55],"reduces":[56],"to":[57,68,93,140],"Sobolev":[60],"seminorm":[61],"can":[63],"allow":[64],"jump":[65],"discontinuities,":[66],"leading":[67],"existence":[69],"results":[70],"broad":[72],"classes":[73],"source":[75],"target":[77],"measures.":[78],"derive":[80,147],"first-order":[81,100],"optimality":[82],"conditions":[83],"analyze":[85],"vanishing-regularization":[87],"limit.":[88],"functionals":[91],"$\u0393$-converge":[92],"classical":[95],"problem,":[97],"while":[98],"$\u0393$-limit":[101],"selects,":[102],"whenever":[103],"they":[104],"exist,":[105],"minimizers":[108],"with":[109],"minimal":[110],"energy.":[112],"When":[113],"no":[114],"such":[115],"minimizer":[116],"exists,":[117],"we":[118,146],"identify":[119],"different":[121],"asymptotic":[122],"regime":[123],"establish":[125],"sharp":[127],"scaling":[128],"law":[129],"in":[130],"prototypical":[132],"mass-splitting":[133],"example.":[134],"Finally,":[135],"after":[136],"lifting":[137],"problem":[139],"product":[142],"plans,":[145],"dual":[149],"formulation":[150],"using":[151],"cone":[153],"copositive":[155],"functions":[156],"propose":[158],"fixed-point":[160],"numerical":[161],"scheme":[162],"illustrating":[163],"regularization.":[165]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}