{"id":"https://openalex.org/W4400422079","doi":"https://doi.org/10.1007/s10915-024-02600-7","title":"Inexact Fixed-Point Proximity Algorithm for the $$\\ell _0$$ Sparse Regularization Problem","display_name":"Inexact Fixed-Point Proximity Algorithm for the $$\\ell _0$$ Sparse Regularization Problem","publication_year":2024,"publication_date":"2024-07-08","ids":{"openalex":"https://openalex.org/W4400422079","doi":"https://doi.org/10.1007/s10915-024-02600-7"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-024-02600-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10915-024-02600-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02600-7.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02600-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113204551","display_name":"Ronglong Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I81365321","display_name":"Old Dominion University","ror":"https://ror.org/04zjtrb98","country_code":"US","type":"education","lineage":["https://openalex.org/I81365321"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ronglong Fang","raw_affiliation_strings":["Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA","institution_ids":["https://openalex.org/I81365321"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026572582","display_name":"Yuesheng Xu","orcid":"https://orcid.org/0000-0003-3965-3087"},"institutions":[{"id":"https://openalex.org/I81365321","display_name":"Old Dominion University","ror":"https://ror.org/04zjtrb98","country_code":"US","type":"education","lineage":["https://openalex.org/I81365321"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuesheng Xu","raw_affiliation_strings":["Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA","institution_ids":["https://openalex.org/I81365321"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002115537","display_name":"Mingsong Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I81365321","display_name":"Old Dominion University","ror":"https://ror.org/04zjtrb98","country_code":"US","type":"education","lineage":["https://openalex.org/I81365321"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingsong Yan","raw_affiliation_strings":["Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA","institution_ids":["https://openalex.org/I81365321"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113204551"],"corresponding_institution_ids":["https://openalex.org/I81365321"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3399,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52776378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"100","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"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":0.9979000091552734,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973999857902527,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9919000267982483,"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/algorithm","display_name":"Algorithm","score":0.8093557357788086},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5601739287376404},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4952632486820221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4516323506832123},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4485979974269867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4374963045120239},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23062822222709656},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15520474314689636}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.8093557357788086},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5601739287376404},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4952632486820221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4516323506832123},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4485979974269867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4374963045120239},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23062822222709656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15520474314689636}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-024-02600-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10915-024-02600-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02600-7.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.odu.edu:mathstat_fac_pubs-1260","is_oa":true,"landing_page_url":"https://digitalcommons.odu.edu/mathstat_fac_pubs/257","pdf_url":null,"source":{"id":"https://openalex.org/S4377196314","display_name":"ODU Digital Commons (Old Dominion University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I81365321","host_organization_name":"Old Dominion University","host_organization_lineage":["https://openalex.org/I81365321"],"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":"Mathematics & Statistics Faculty Publications","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10915-024-02600-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10915-024-02600-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02600-7.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4043512067","display_name":null,"funder_award_id":"DMS-2208386","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400422079.pdf"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W948098727","https://openalex.org/W1489128386","https://openalex.org/W1543180643","https://openalex.org/W1580765281","https://openalex.org/W1967138577","https://openalex.org/W1971478618","https://openalex.org/W1978333359","https://openalex.org/W1983772857","https://openalex.org/W1984866494","https://openalex.org/W1990693901","https://openalex.org/W1997301483","https://openalex.org/W2016859302","https://openalex.org/W2018342351","https://openalex.org/W2019786292","https://openalex.org/W2020925091","https://openalex.org/W2021603736","https://openalex.org/W2022541060","https://openalex.org/W2028781966","https://openalex.org/W2038497950","https://openalex.org/W2045079045","https://openalex.org/W2059448319","https://openalex.org/W2074214991","https://openalex.org/W2074682976","https://openalex.org/W2090614493","https://openalex.org/W2092663520","https://openalex.org/W2094621673","https://openalex.org/W2112796928","https://openalex.org/W2115755118","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2138216979","https://openalex.org/W2147850450","https://openalex.org/W2153635508","https://openalex.org/W2164647001","https://openalex.org/W2244987555","https://openalex.org/W2763081248","https://openalex.org/W2804685622","https://openalex.org/W2900779353","https://openalex.org/W2944887911","https://openalex.org/W2962853966","https://openalex.org/W2972293876","https://openalex.org/W3106361977","https://openalex.org/W4229650096","https://openalex.org/W4246327874","https://openalex.org/W4250955649","https://openalex.org/W4255272544","https://openalex.org/W4282813188","https://openalex.org/W4283314725","https://openalex.org/W4292363360","https://openalex.org/W4320913585"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W4387635768"],"abstract_inverted_index":{"Abstract":[0],"We":[1,129,155,179],"study":[2],"inexact":[3,126,153,168,234],"fixed-point":[4],"proximity":[5,99,119],"algorithms":[6,86,183],"for":[7,87,97,138,184],"solving":[8,88],"a":[9,48,53,157,172],"class":[10],"of":[11,47,56,94,101,117,141,151,175,187,209,218,239,254,259],"sparse":[12],"regularization":[13,68],"problems":[14,90],"involving":[15],"the":[16,28,45,57,89,92,98,106,118,135,142,152,162,166,176,181,207,210,219,232,240,260],"$$\\ell":[17,29,58,72,220,242],"_0$$":[18,30,59,73,221],"<mml:math":[19,31,60,74,222,244],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[20,32,61,75,223,245],"<mml:msub>":[21,33,62,76,224,246],"<mml:mi>\u2113</mml:mi>":[22,34,63,77,225,247],"<mml:mn>0</mml:mn>":[23,35,64,78,226],"</mml:msub>":[24,36,65,79,227,249],"</mml:math>":[25,37,66,80,228,250],"norm.":[26],"Specifically,":[27],"model":[38,81],"has":[39],"an":[40,71],"objective":[41,107],"function":[42],"that":[43,160,215],"is":[44,82],"sum":[46],"convex":[49,102],"fidelity":[50],"term":[51],"and":[52,193,200,213,257],"Moreau":[54],"envelope":[55],"norm":[67],"term.":[69],"Such":[70],"non-convex.":[83],"Existing":[84],"exact":[85],"require":[91],"availability":[93],"closed-form":[95],"formulas":[96,111],"operator":[100,120],"functions":[103],"involved":[104],"in":[105,131,190,252],"function.":[108],"When":[109],"such":[110],"are":[112],"not":[113],"available,":[114],"numerical":[115,136,204],"computation":[116],"becomes":[121],"inevitable.":[122],"This":[123],"leads":[124],"to":[125,147,171],"iteration":[127,143],"algorithms.":[128,154],"investigate":[130],"this":[132],"paper":[133],"how":[134],"error":[137],"every":[139],"step":[140],"should":[144],"be":[145],"controlled":[146],"ensure":[148],"global":[149,237],"convergence":[150,208],"establish":[156],"theoretical":[158],"result":[159],"guarantees":[161],"sequence":[163],"generated":[164],"by":[165,231],"proposed":[167,182,211,233],"algorithm":[169,212,235],"converges":[170],"local":[173,216],"minimizer":[174],"optimization":[177],"problem.":[178],"implement":[180],"three":[185],"applications":[186],"practical":[188],"importance":[189],"machine":[191],"learning":[192],"image":[194,201],"science,":[195],"which":[196],"include":[197],"regression,":[198],"classification,":[199],"deblurring.":[202],"The":[203],"results":[205],"demonstrate":[206],"confirm":[214],"minimizers":[217,238],"models":[229],"found":[230],"outperform":[236],"corresponding":[241],"_1$$":[243],"<mml:mn>1</mml:mn>":[248],"models,":[251],"terms":[253],"approximation":[255],"accuracy":[256],"sparsity":[258],"solutions.":[261]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
