{"id":"https://openalex.org/W2910941978","doi":"https://doi.org/10.1137/18m1183388","title":"Sparse Inverse Problems over Measures: Equivalence of the Conditional Gradient and Exchange Methods","display_name":"Sparse Inverse Problems over Measures: Equivalence of the Conditional Gradient and Exchange Methods","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2910941978","doi":"https://doi.org/10.1137/18m1183388","mag":"2910941978"},"language":"en","primary_location":{"id":"doi:10.1137/18m1183388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1183388","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/268204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086280273","display_name":"Armin Eftekhari","orcid":"https://orcid.org/0000-0001-8202-6316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Armin Eftekhari","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8202-6316","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101752265","display_name":"Andrew Thompson","orcid":"https://orcid.org/0000-0002-4580-0357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Thompson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4580-0357","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6817,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81877031,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"29","issue":"2","first_page":"1329","last_page":"1349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7083853483200073},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6290654540061951},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5607603192329407},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49942946434020996},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47876158356666565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4080694317817688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2618696093559265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.25928330421447754},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20909690856933594}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7083853483200073},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6290654540061951},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5607603192329407},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49942946434020996},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47876158356666565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4080694317817688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2618696093559265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25928330421447754},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20909690856933594},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1183388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1183388","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:268204","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/268204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:268204","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/268204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4072067573","display_name":null,"funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G6522507952","display_name":null,"funder_award_id":"SF019","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G8597009950","display_name":null,"funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1963481290","https://openalex.org/W2004239023","https://openalex.org/W2023653074","https://openalex.org/W2026035956","https://openalex.org/W2032916024","https://openalex.org/W2038589630","https://openalex.org/W2069808690","https://openalex.org/W2075887074","https://openalex.org/W2103955025","https://openalex.org/W2119499160","https://openalex.org/W2119667497","https://openalex.org/W2127271355","https://openalex.org/W2136885855","https://openalex.org/W2155447220","https://openalex.org/W2167077875","https://openalex.org/W2167208435","https://openalex.org/W2524857034","https://openalex.org/W2565293665","https://openalex.org/W2585868105","https://openalex.org/W2605512869","https://openalex.org/W2608482034","https://openalex.org/W2914166403","https://openalex.org/W2952019053","https://openalex.org/W2962898451","https://openalex.org/W2963772835","https://openalex.org/W2963809997","https://openalex.org/W2964177174","https://openalex.org/W2964325628"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2896134808","https://openalex.org/W3103861421","https://openalex.org/W4211228991","https://openalex.org/W2949110394","https://openalex.org/W2353790329","https://openalex.org/W1963802308","https://openalex.org/W3214543110","https://openalex.org/W4226153041","https://openalex.org/W2009166380"],"abstract_inverted_index":{"We":[0,49],"study":[1],"an":[2,163],"optimization":[3],"program":[4,19],"over":[5],"nonnegative":[6],"Borel":[7],"measures":[8],"that":[9,51,122],"encourages":[10],"sparsity":[11],"in":[12,21,41,65,108,129,144],"its":[13,77],"solution.":[14],"Efficient":[15],"solvers":[16],"for":[17,119,157],"this":[18,59,109,136],"are":[20],"increasing":[22],"demand,":[23],"as":[24,62,172],"it":[25],"arises":[26],"when":[27],"learning":[28],"from":[29],"data":[30],"generated":[31],"by":[32],"a":[33,36,82,115],"\u201ccontinuum-of-subspaces\u201d":[34],"model,":[35],"recent":[37],"trend":[38],"with":[39],"applications":[40],"signal":[42],"processing,":[43],"machine":[44],"learning,":[45],"and":[46,138],"high-dimensional":[47],"statistics.":[48],"prove":[50],"the":[52,66,71,95,102,105,120,130,133,139,145,149,155,173],"conditional":[53],"gradient":[54],"method":[55,73],"(CGM)":[56],"applied":[57,75],"to":[58,70,76,94,113,148],"infinite-dimensional":[60,92,158],"program,":[61],"proposed":[63],"recently":[64],"literature,":[67],"is":[68,81,123,169],"equivalent":[69],"exchange":[72],"(EM)":[74],"Lagrangian":[78],"dual,":[79],"which":[80,160],"semi-infinite":[83,99],"program.":[84],"In":[85],"doing":[86],"so,":[87],"we":[88],"formally":[89],"connect":[90],"such":[91],"programs":[93],"well-established":[96],"field":[97],"of":[98,117,151,154],"programming.":[100],"On":[101,132],"one":[103],"hand,":[104,135],"equivalence":[106],"established":[107],"paper":[110],"allows":[111],"us":[112],"provide":[114],"rate":[116],"convergence":[118],"EM":[121],"more":[124],"general":[125],"than":[126],"those":[127],"existing":[128],"literature.":[131],"other":[134],"connection":[137],"resulting":[140],"geometric":[141],"insights":[142],"might":[143],"future":[146],"lead":[147],"design":[150],"improved":[152],"variants":[153],"CGM":[156,168],"programs,":[159],"has":[161],"been":[162],"active":[164],"research":[165],"topic.":[166],"The":[167],"also":[170],"known":[171],"Frank--Wolfe":[174],"algorithm.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
