{"id":"https://openalex.org/W3179233143","doi":"https://doi.org/10.1007/s10898-022-01143-1","title":"Partial gradient optimal thresholding algorithms for a class of sparse optimization problems","display_name":"Partial gradient optimal thresholding algorithms for a class of sparse optimization problems","publication_year":2022,"publication_date":"2022-02-23","ids":{"openalex":"https://openalex.org/W3179233143","doi":"https://doi.org/10.1007/s10898-022-01143-1","mag":"3179233143"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-022-01143-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01143-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01143-1.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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/s10898-022-01143-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001341683","display_name":"Nan Meng","orcid":"https://orcid.org/0000-0001-7232-9348"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nan Meng","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057733991","display_name":"Yun-Bin Zhao","orcid":"https://orcid.org/0000-0002-2388-9047"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yun-Bin Zhao","raw_affiliation_strings":["Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-2388-9047","affiliations":[{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586","https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041987187","display_name":"Michal Ko\u010dvara","orcid":"https://orcid.org/0000-0003-4414-0083"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michal Ko\u010dvara","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066663652","display_name":"Zhongfeng Sun","orcid":"https://orcid.org/0000-0003-1794-7869"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongfeng Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University of Technology, Zibo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University of Technology, Zibo, China","institution_ids":["https://openalex.org/I119203015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057733991"],"corresponding_institution_ids":["https://openalex.org/I4210099586","https://openalex.org/I4210116924"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":1.6785,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80137543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"84","issue":"2","first_page":"393","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/thresholding","display_name":"Thresholding","score":0.923617959022522},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6320005059242249},{"id":"https://openalex.org/keywords/balanced-histogram-thresholding","display_name":"Balanced histogram thresholding","score":0.618639349937439},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5752032995223999},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4962344765663147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4922298491001129},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.492213636636734},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47165647149086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3568650484085083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34140580892562866},{"id":"https://openalex.org/keywords/histogram","display_name":"Histogram","score":0.13974541425704956},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12762731313705444},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10002082586288452}],"concepts":[{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.923617959022522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6320005059242249},{"id":"https://openalex.org/C202577368","wikidata":"https://www.wikidata.org/wiki/Q2576067","display_name":"Balanced histogram thresholding","level":5,"score":0.618639349937439},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5752032995223999},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4962344765663147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4922298491001129},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.492213636636734},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47165647149086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3568650484085083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34140580892562866},{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.13974541425704956},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12762731313705444},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10002082586288452},{"id":"https://openalex.org/C136943445","wikidata":"https://www.wikidata.org/wiki/Q1970240","display_name":"Histogram equalization","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-022-01143-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01143-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01143-1.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01143-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-022-01143-1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/4017c37c-c436-4f68-a3c1-f5ac1dd0d9be","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/4017c37c-c436-4f68-a3c1-f5ac1dd0d9be","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"Meng, N, Zhao, Y-B, Kocvara, M & Sun, Z 2022, 'Partial gradient optimal thresholding algorithms for a class of sparse optimization problems', Journal of Global Optimization, vol. 84, no. 2, pp. 393-413. https://doi.org/10.1007/s10898-022-01143-1","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/4017c37c-c436-4f68-a3c1-f5ac1dd0d9be","is_oa":true,"landing_page_url":"https://birmingham.elsevierpure.com/en/publications/4017c37c-c436-4f68-a3c1-f5ac1dd0d9be","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1007/s10898-022-01143-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01143-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01143-1.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4205807689","display_name":"\u6570\u636e\u538b\u7f29\u4e0e\u91cd\u6784\u7684\u65b0\u4e00\u4ee3\u9ad8\u6027\u80fd\u4f18\u5316\u7b97\u6cd5","funder_award_id":"12071307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3179233143.pdf","grobid_xml":"https://content.openalex.org/works/W3179233143.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W340244495","https://openalex.org/W653768339","https://openalex.org/W1527917680","https://openalex.org/W1596877211","https://openalex.org/W1969436875","https://openalex.org/W1977520307","https://openalex.org/W1980454827","https://openalex.org/W1981487911","https://openalex.org/W2025079166","https://openalex.org/W2038517753","https://openalex.org/W2052724630","https://openalex.org/W2078204800","https://openalex.org/W2095978736","https://openalex.org/W2107861471","https://openalex.org/W2123023890","https://openalex.org/W2127271355","https://openalex.org/W2129131372","https://openalex.org/W2140856955","https://openalex.org/W2144006746","https://openalex.org/W2145096794","https://openalex.org/W2146842127","https://openalex.org/W2160979406","https://openalex.org/W2161208647","https://openalex.org/W2163107063","https://openalex.org/W2289917018","https://openalex.org/W2296052754","https://openalex.org/W2486545612","https://openalex.org/W2526012566","https://openalex.org/W2540784894","https://openalex.org/W2784401476","https://openalex.org/W2874258323","https://openalex.org/W2910785486","https://openalex.org/W2962959174","https://openalex.org/W2963322354","https://openalex.org/W2963334250","https://openalex.org/W2964292648","https://openalex.org/W2998383793","https://openalex.org/W3002118509","https://openalex.org/W3015654455","https://openalex.org/W3040238575","https://openalex.org/W3099257477","https://openalex.org/W3137617174","https://openalex.org/W3139784355","https://openalex.org/W3161751243","https://openalex.org/W4300263211"],"related_works":["https://openalex.org/W2750730210","https://openalex.org/W3103243916","https://openalex.org/W2295077625","https://openalex.org/W4299814392","https://openalex.org/W2757003988","https://openalex.org/W2900829073","https://openalex.org/W2770684271","https://openalex.org/W2353716847","https://openalex.org/W2151415411","https://openalex.org/W3049769024"],"abstract_inverted_index":{"Abstract":[0],"The":[1,163,178],"optimization":[2,14,204],"problems":[3,205],"with":[4],"a":[5,9,25,38,47,56,60,69,77,99,104,109,123],"sparsity":[6],"constraint":[7],"is":[8,50,165,210,223],"class":[10],"of":[11,19,59,103,112,132,168,198],"important":[12,65],"global":[13],"problems.":[15],"A":[16],"typical":[17],"type":[18],"thresholding":[20,49,54,78,94,125,137,153],"algorithms":[21,187],"for":[22,184],"solving":[23],"such":[24,76],"problem":[26],"adopts":[27],"the":[28,92,115,118,129,148,169,173,185,202,220],"traditional":[29],"full":[30],"steepest":[31],"descent":[32],"direction":[33,36,40],"or":[34],"Newton-like":[35],"as":[37,122],"search":[39],"to":[41,98,107,146,201,227],"generate":[42],"an":[43,166],"iterate":[44],"on":[45],"which":[46],"certain":[48],"performed.":[51],"Traditional":[52],"hard":[53,93,133],"discards":[55],"large":[57],"part":[58],"vector,":[61],"and":[62,135,138,156,172,182,225],"thus":[63],"some":[64],"information":[66],"contained":[67],"in":[68,75,83,160,191],"dense":[70,105],"vector":[71,101,106],"has":[72],"been":[73,189],"lost":[74],"process.":[79],"Recent":[80],"study":[81],"(Zhao":[82],"SIAM":[84],"J":[85],"Optim":[86],"30(1):":[87],"31\u201355,":[88],"2020)":[89],"shows":[90],"that":[91,219],"should":[95],"be":[96],"applied":[97],"compressible":[100],"instead":[102],"avoid":[108],"big":[110],"loss":[111],"information.":[113],"On":[114],"other":[116],"hand,":[117],"optimal":[119,152,174],"k":[120,175],"-thresholding":[121,176],"novel":[124],"technique":[126],"may":[127],"overcome":[128],"intrinsic":[130],"drawback":[131],"thresholding,":[134],"performs":[136],"objective":[139],"function":[140],"minimization":[141],"simultaneously.":[142],"This":[143],"motivates":[144],"us":[145],"propose":[147],"so-called":[149],"partial":[150,170],"gradient":[151,171],"(PGOT)":[154],"method":[155],"its":[157],"relaxed":[158],"versions":[159],"this":[161,192],"paper.":[162],"PGOT":[164],"integration":[167],"technique.":[177],"solution":[179],"error":[180],"bound":[181],"convergence":[183],"proposed":[186,221],"have":[188],"established":[190],"paper":[193],"under":[194],"suitable":[195],"conditions.":[196],"Application":[197],"our":[199],"results":[200,214],"sparse":[203],"arising":[206],"from":[207,215],"signal":[208],"recovery":[209],"also":[211],"discussed.":[212],"Experiment":[213],"synthetic":[216],"data":[217],"indicate":[218],"algorithm":[222],"efficient":[224],"comparable":[226],"several":[228],"existing":[229],"algorithms.":[230]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}