{"id":"https://openalex.org/W4379259748","doi":"https://doi.org/10.1137/24m167634x","title":"Sparse Approximation of the Lieb Functional with Moment Constraints","display_name":"Sparse Approximation of the Lieb Functional with Moment Constraints","publication_year":2026,"publication_date":"2026-06-03","ids":{"openalex":"https://openalex.org/W4379259748","doi":"https://doi.org/10.1137/24m167634x"},"language":"en","primary_location":{"id":"doi:10.1137/24m167634x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m167634x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2306.00806","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043821615","display_name":"Virginie Ehrlacher","orcid":"https://orcid.org/0000-0001-6540-4784"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Virginie Ehrlacher","raw_affiliation_strings":["CERMICS, Ecole Nationale des Ponts et Chauss\u00e9es, 77420 Champs-sur-Marne, France, and ParMA, Inria Saclay, 91405 Orsay, France"],"raw_orcid":"https://orcid.org/0000-0001-6540-4784","affiliations":[{"raw_affiliation_string":"CERMICS, Ecole Nationale des Ponts et Chauss\u00e9es, 77420 Champs-sur-Marne, France, and ParMA, Inria Saclay, 91405 Orsay, France","institution_ids":["https://openalex.org/I142631665","https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064926820","display_name":"Luca Nenna","orcid":"https://orcid.org/0000-0003-2540-1700"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210090571","display_name":"Institut des Sciences des Plantes de Paris Saclay","ror":"https://ror.org/00ajjta07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210088668","https://openalex.org/I4210090571","https://openalex.org/I88467170"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luca Nenna","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay, CNRS, Laboratoire de math\u00e9matiques d\u2019Orsay, ParMA, Inria Saclay, 91405 Orsay, France, and Institut Universitaire de France 75005 Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-2540-1700","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay, CNRS, Laboratoire de math\u00e9matiques d\u2019Orsay, ParMA, Inria Saclay, 91405 Orsay, France, and Institut Universitaire de France 75005 Paris, France","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I277688954","https://openalex.org/I4210090571","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01446009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"3","first_page":"2865","last_page":"2893"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.38269999623298645,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.38269999623298645,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.09589999914169312,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.07069999724626541,"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/trace","display_name":"TRACE (psycholinguistics)","score":0.5666438937187195},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5643078684806824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5455774664878845},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4959791600704193},{"id":"https://openalex.org/keywords/density-functional-theory","display_name":"Density functional theory","score":0.49142682552337646},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45385488867759705},{"id":"https://openalex.org/keywords/orbital-free-density-functional-theory","display_name":"Orbital-free density functional theory","score":0.4514521360397339},{"id":"https://openalex.org/keywords/hybrid-functional","display_name":"Hybrid functional","score":0.37314701080322266},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3448783755302429},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32633793354034424},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.31171178817749023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2455105185508728},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24346235394477844}],"concepts":[{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5666438937187195},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5643078684806824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5455774664878845},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4959791600704193},{"id":"https://openalex.org/C152365726","wikidata":"https://www.wikidata.org/wiki/Q1048589","display_name":"Density functional theory","level":2,"score":0.49142682552337646},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45385488867759705},{"id":"https://openalex.org/C104970782","wikidata":"https://www.wikidata.org/wiki/Q7100054","display_name":"Orbital-free density functional theory","level":4,"score":0.4514521360397339},{"id":"https://openalex.org/C22693506","wikidata":"https://www.wikidata.org/wiki/Q3075290","display_name":"Hybrid functional","level":3,"score":0.37314701080322266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3448783755302429},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32633793354034424},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.31171178817749023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2455105185508728},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24346235394477844},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/24m167634x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m167634x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2306.00806","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.00806","pdf_url":"https://arxiv.org/pdf/2306.00806","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04131066v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04131066","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-04131066","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-04131066v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04131066v2/document","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2306.00806","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2306.00806","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2306.00806","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.00806","pdf_url":"https://arxiv.org/pdf/2306.00806","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.4099999964237213,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2361257913","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G398379830","display_name":null,"funder_award_id":"101077204","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G6038677436","display_name":null,"funder_award_id":"ANR-23-CE46-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7683707404","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320324252","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503"},{"id":"https://openalex.org/F4320324478","display_name":"Fondation Math\u00e9matique Jacques Hadamard","ror":"https://ror.org/0153me927"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4379259748.pdf","grobid_xml":"https://content.openalex.org/works/W4379259748.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2013110429","https://openalex.org/W2025208242","https://openalex.org/W2733294612","https://openalex.org/W2005532699","https://openalex.org/W2071966572","https://openalex.org/W2008920194","https://openalex.org/W2090366060","https://openalex.org/W4380551274","https://openalex.org/W2086725245","https://openalex.org/W2032232804"],"abstract_inverted_index":{"The":[0,31],"aim":[1],"of":[2,29,43,55,70,82,99,106,114,129,147,154,157,179,196,208,214,222,230,240,246,257],"this":[3,75,130],"paper":[4],"is":[5,17,77,141],"to":[6,39,120,173,193,219,233,270],"present":[7],"new":[8],"sparsity":[9],"results":[10],"about":[11],"the":[12,44,68,71,80,97,104,121,136,151,155,166,174,180,194,206,212,215,220,223,228,243,247,254,258],"so-called":[13,45],"Lieb":[14,32,38,72,181,225],"functional,":[15],"which":[16,58,89],"a":[18,41,53,63,83,92,127,144,264],"key":[19],"quantity":[20],"in":[21,268],"Density":[22],"Functional":[23],"Theory":[24],"for":[25,52,74],"electronic":[26,50,107,123,167],"structure":[27],"calculations":[28],"molecules.":[30],"functional":[33,73,183,217,226],"was":[34],"actually":[35],"shown":[36],"by":[37,143],"be":[40,60],"convexification":[42],"L\u00e9vy-Lieb":[46],"functional.":[47],"Given":[48],"an":[49],"density":[51,65,76],"system":[54],"$N$":[56],"electrons,":[57],"may":[59],"seen":[61],"as":[62,79,91,186,227],"probability":[64],"on":[66,96,103,150,165,205,242],"$\\mathbb{R}^3$,":[67],"value":[69,213,221],"defined":[78,95],"solution":[81],"quantum":[84,131],"multi-marginal":[85],"optimal":[86,132],"transport":[87,133],"problem,":[88],"reads":[90],"minimization":[93],"problem":[94,134,261],"set":[98,156,207],"trace-class":[100],"operators":[101,187],"acting":[102],"space":[105],"wave-functions":[108],"that":[109,184,211],"are":[110],"anti-symmetric":[111],"$L^2$":[112],"functions":[113,210],"$\\mathbb{R}^{3N}$,":[115],"with":[116,188],"partial":[117,138,152],"trace":[118,139,153],"equal":[119,192],"prescribed":[122],"density.":[124],"We":[125,159,199,235,251],"introduce":[126,263],"relaxation":[128],"where":[135],"full":[137],"constraint":[140],"replaced":[142],"finite":[145],"number":[146,195,229],"moment":[148,176,197,209],"constraints":[149],"operators.":[158],"show":[160],"that,":[161],"under":[162,202],"mild":[163],"assumptions":[164,204],"density,":[168],"there":[169],"exist":[170],"sparse":[171],"minimizers":[172],"resulting":[175],"constrained":[177],"approximation":[178,245],"(MCAL)":[182],"read":[185],"rank":[189],"at":[190],"most":[191],"constraints.":[198],"also":[200,236],"prove":[201,237],"appropriate":[203],"MCAL":[216],"converges":[218],"exact":[224],"moments":[231],"go":[232],"infinity.":[234],"some":[238,272],"rates":[239],"convergence":[241],"associated":[244,259],"ground":[248],"state":[249],"energy.":[250],"finally":[252],"study":[253],"mathematical":[255],"properties":[256],"dual":[260],"and":[262],"suitable":[265],"numerical":[266],"algorithm":[267],"order":[269],"solve":[271],"simple":[273],"toy":[274],"models.":[275]},"counts_by_year":[],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}