{"id":"https://openalex.org/W4309542894","doi":"https://doi.org/10.3389/fams.2022.1031039","title":"Bregman iterative regularization using model functions for nonconvex nonsmooth optimization","display_name":"Bregman iterative regularization using model functions for nonconvex nonsmooth optimization","publication_year":2022,"publication_date":"2022-11-22","ids":{"openalex":"https://openalex.org/W4309542894","doi":"https://doi.org/10.3389/fams.2022.1031039"},"language":"en","primary_location":{"id":"doi:10.3389/fams.2022.1031039","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2022.1031039","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2022.1031039/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fams.2022.1031039/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002304307","display_name":"Haoxing Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haoxing Yang","raw_affiliation_strings":["Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100323420","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0002-1803-3148"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100373288","display_name":"Hongxia Wang","orcid":"https://orcid.org/0000-0003-0720-3305"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongxia Wang","raw_affiliation_strings":["Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102893559","display_name":"Lizhi Cheng","orcid":"https://orcid.org/0000-0002-8371-066X"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lizhi Cheng","raw_affiliation_strings":["Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100323420"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12675153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9944000244140625,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9652000069618225,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7177790403366089},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7022531032562256},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.5458555221557617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5378097891807556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5340643525123596},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5258967280387878},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5062054991722107},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4983837604522705},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4489966928958893},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41575708985328674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3969540596008301},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37035369873046875},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10597878694534302},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1012398898601532}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7177790403366089},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7022531032562256},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.5458555221557617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5378097891807556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5340643525123596},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5258967280387878},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5062054991722107},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4983837604522705},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4489966928958893},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41575708985328674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3969540596008301},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37035369873046875},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10597878694534302},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1012398898601532},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3389/fams.2022.1031039","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2022.1031039","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2022.1031039/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d466a88c529e44f790c70fd847e94adc","is_oa":true,"landing_page_url":"https://doaj.org/article/d466a88c529e44f790c70fd847e94adc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Applied Mathematics and Statistics, Vol 8 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fams.2022.1031039","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2022.1031039","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2022.1031039/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4792774345","display_name":null,"funder_award_id":"2020-JCJQ-ZD-029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5848258319","display_name":null,"funder_award_id":"0 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6221780053","display_name":null,"funder_award_id":"11971","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8498444804","display_name":null,"funder_award_id":"11971480","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8891886155","display_name":null,"funder_award_id":"2020-JCJQ","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8980960326","display_name":null,"funder_award_id":"61977065","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/W4309542894.pdf","grobid_xml":"https://content.openalex.org/works/W4309542894.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1934819276","https://openalex.org/W1972552174","https://openalex.org/W1996287810","https://openalex.org/W2011181254","https://openalex.org/W2021361347","https://openalex.org/W2022164193","https://openalex.org/W2027982384","https://openalex.org/W2033468335","https://openalex.org/W2067272684","https://openalex.org/W2075826622","https://openalex.org/W2090376964","https://openalex.org/W2123825652","https://openalex.org/W2142949395","https://openalex.org/W2163803752","https://openalex.org/W2551153860","https://openalex.org/W2595897327","https://openalex.org/W2763081248","https://openalex.org/W2884803963","https://openalex.org/W2964211254","https://openalex.org/W2964222150","https://openalex.org/W2977046017","https://openalex.org/W2982573148","https://openalex.org/W3099756117","https://openalex.org/W3163340401","https://openalex.org/W3215317737","https://openalex.org/W4223588778","https://openalex.org/W4249667877","https://openalex.org/W4295694258","https://openalex.org/W6684190412"],"related_works":["https://openalex.org/W2790371392","https://openalex.org/W2949110699","https://openalex.org/W4298203258","https://openalex.org/W2951306248","https://openalex.org/W1891027457","https://openalex.org/W4221160903","https://openalex.org/W2576451984","https://openalex.org/W2937971365","https://openalex.org/W2534083081","https://openalex.org/W3095191489"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,34,62,75,92],"propose":[4,102],"a":[5,24,43],"new":[6],"algorithm":[7,83],"called":[8],"ModelBI":[9],"by":[10],"blending":[11],"the":[12,18,36,47,53,59,64,77,81,85,88,110,115],"Bregman":[13,65],"iterative":[14,66],"regularization":[15,67],"method":[16],"and":[17,101,113],"model":[19,37],"function":[20,38],"technique":[21],"for":[22],"solving":[23],"class":[25],"of":[26,80,87,96,117],"nonconvex":[27],"nonsmooth":[28,97],"optimization":[29],"problems.":[30],"On":[31,58],"one":[32],"hand,":[33,61],"use":[35,63],"technique,":[39],"which":[40],"is":[41],"essentially":[42],"first-order":[44],"approximation":[45],"to":[46,50,68],"objective":[48],"function,":[49],"go":[51],"beyond":[52],"traditional":[54],"Lipschitz":[55],"gradient":[56],"continuity.":[57],"other":[60],"generate":[69],"solutions":[70],"fitting":[71],"certain":[72],"structures.":[73],"Theoretically,":[74],"show":[76],"global":[78,111],"convergence":[79,112],"proposed":[82,119],"with":[84],"help":[86],"Kurdyka-\u0141ojasiewicz":[89],"property.":[90],"Finally,":[91],"consider":[93],"two":[94],"kinds":[95],"phase":[98],"retrieval":[99],"problems":[100],"an":[103],"explicit":[104],"iteration":[105],"scheme.":[106],"Numerical":[107],"results":[108],"verify":[109],"illustrate":[114],"potential":[116],"our":[118],"algorithm.":[120]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
