{"id":"https://openalex.org/W2054961232","doi":"https://doi.org/10.1155/2015/175254","title":"Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators","display_name":"Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2054961232","doi":"https://doi.org/10.1155/2015/175254","mag":"2054961232"},"language":"lv","primary_location":{"id":"doi:10.1155/2015/175254","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/175254","pdf_url":"https://downloads.hindawi.com/journals/jam/2015/175254.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2015/175254.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015160682","display_name":"Yang Cai-ping","orcid":null},"institutions":[{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caiping Yang","raw_affiliation_strings":["College of Science, Civil Aviation University of China, Tianjin 300300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin 300300, China","institution_ids":["https://openalex.org/I28813325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100930532","display_name":"Songnian He","orcid":null},"institutions":[{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Songnian He","raw_affiliation_strings":["College of Science, Civil Aviation University of China, Tianjin 300300, China","Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin 300300, China","institution_ids":["https://openalex.org/I28813325"]},{"raw_affiliation_string":"Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China","institution_ids":["https://openalex.org/I28813325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100930532"],"corresponding_institution_ids":["https://openalex.org/I28813325"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07233267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2015","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9954000115394592,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9894999861717224,"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/algorithm","display_name":"Algorithm","score":0.6718834042549133},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34820282459259033},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33899903297424316}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6718834042549133},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34820282459259033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33899903297424316}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2015/175254","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/175254","pdf_url":"https://downloads.hindawi.com/journals/jam/2015/175254.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1429105544","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1429105544","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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:RePEc:hin:jnljam:175254","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2015/175254.xml","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:doaj.org/article:f004de8f80e0424981fc1e8acd34b6ad","is_oa":true,"landing_page_url":"https://doaj.org/article/f004de8f80e0424981fc1e8acd34b6ad","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2015 (2015)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2015/175254","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/175254","pdf_url":"https://downloads.hindawi.com/journals/jam/2015/175254.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.550000011920929,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1364243576","display_name":null,"funder_award_id":"3122014K010","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054961232.pdf","grobid_xml":"https://content.openalex.org/works/W2054961232.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W140076683","https://openalex.org/W631421241","https://openalex.org/W1488903562","https://openalex.org/W1516681311","https://openalex.org/W1546168022","https://openalex.org/W1972679045","https://openalex.org/W1979064790","https://openalex.org/W1985348591","https://openalex.org/W1987665513","https://openalex.org/W2008021048","https://openalex.org/W2008702252","https://openalex.org/W2019624210","https://openalex.org/W2033943991","https://openalex.org/W2051948401","https://openalex.org/W2064176740","https://openalex.org/W2064958771","https://openalex.org/W2093246563","https://openalex.org/W4231269780"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"Consider":[0],"the":[1,14,105,119,127,156,172],"variational":[2,66],"inequality<mml:math":[3],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,11,16,23,26,41,43,54,107,109,122,145,154],"id=\"M1\"><mml:mtext>V</mml:mtext><mml:mtext>I</mml:mtext><mml:mo":[5],"stretchy=\"false\">(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>F</mml:mi><mml:mo":[6],"stretchy=\"false\">)</mml:mo></mml:math>of":[7],"finding":[8],"a":[9,28,32,37,45,69,112,130],"point<mml:math":[10],"id=\"M2\"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi":[12],"mathvariant=\"normal\">*</mml:mi></mml:mrow></mml:msup><mml:mo>\u2208</mml:mo><mml:mi>C</mml:mi></mml:math>satisfying":[13],"property<mml:math":[15],"id=\"M3\"><mml:mo":[17],"stretchy=\"false\">\u2329</mml:mo><mml:mi>F</mml:mi><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi":[18],"mathvariant=\"normal\">*</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi":[19],"mathvariant=\"normal\">*</mml:mi></mml:mrow></mml:msup><mml:mo":[20],"stretchy=\"false\">\u232a</mml:mo><mml:mo>\u2265</mml:mo><mml:mn>0</mml:mn></mml:math>for":[21],"all<mml:math":[22],"id=\"M4\"><mml:mi>x</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>C</mml:mi></mml:math>,":[24],"where<mml:math":[25],"id=\"M5\"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>is":[27],"level":[29],"set":[30],"of":[31,114,140,158,175],"convex":[33],"function":[34],"defined":[35],"on":[36,50,149],"real":[38],"Hilbert":[39],"space<mml:math":[40],"id=\"M6\"><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>and<mml:math":[42],"id=\"M7\"><mml:mi>F</mml:mi><mml:mo>:</mml:mo><mml:mi>H</mml:mi><mml:mo>\u2192</mml:mo><mml:mi>H</mml:mi></mml:math>is":[44],"boundedly":[46],"Lipschitzian":[47,49],"(i.e.,":[48],"bounded":[51,141,151],"subsets":[52,152],"of<mml:math":[53,144,153],"id=\"M8\"><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>)":[55],"and":[56,61,72,82,89,125,170,177],"strongly":[57],"monotone":[58],"operator.":[59],"He":[60,81,176],"Xu":[62],"proved":[63],"that":[64],"this":[65,78,86,97,167],"inequality":[67],"has":[68],"unique":[70,98],"solution":[71,79],"devised":[73],"iterative":[74,91],"algorithms":[75,92,102,160,165],"to":[76,136],"approximate":[77],"(see":[80],"Xu,":[83],"2009).":[84],"In":[85],"paper,":[87],"relaxed":[88],"self-adaptive":[90,131],"are":[93,161],"proposed":[94],"for":[95],"computing":[96,111],"solution.":[99],"Since":[100],"our":[101,159],"avoid":[103],"calculating":[104],"projection<mml:math":[106],"id=\"M9\"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>(calculating<mml:math":[108],"id=\"M10\"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>by":[110],"sequence":[113],"projections":[115],"onto":[116],"half-spaces":[117],"containing":[118],"original":[120],"domain<mml:math":[121],"id=\"M11\"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>)":[123],"directly":[124],"select":[126],"stepsizes":[128],"through":[129],"way":[132],"(having":[133],"no":[134],"need":[135],"know":[137],"any":[138],"information":[139],"Lipschitz":[142,147],"constants":[143,148],"id=\"M12\"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math>(i.e.,":[146],"some":[150],"id=\"M13\"><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>)),":[155],"implementations":[157],"very":[162],"easy.":[163],"The":[164],"in":[166],"paper":[168],"improve":[169],"extend":[171],"corresponding":[173],"results":[174],"Xu.":[178]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
