{"id":"https://openalex.org/W4283381440","doi":"https://doi.org/10.1080/10556788.2022.2064467","title":"Isotonicity of the proximity operator and stochastic optimization problems in Hilbert quasi-lattices endowed with Lorentz cones","display_name":"Isotonicity of the proximity operator and stochastic optimization problems in Hilbert quasi-lattices endowed with Lorentz cones","publication_year":2022,"publication_date":"2022-04-25","ids":{"openalex":"https://openalex.org/W4283381440","doi":"https://doi.org/10.1080/10556788.2022.2064467"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2022.2064467","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2022.2064467","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090556479","display_name":"Dezhou Kong","orcid":"https://orcid.org/0000-0001-8399-7763"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dezhou Kong","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University","College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0001-8399-7763","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101966878","display_name":"Li Sun","orcid":"https://orcid.org/0000-0002-3589-4898"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Sun","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University","College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100757330","display_name":"Haibin Chen","orcid":"https://orcid.org/0000-0003-2636-2600"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haibin Chen","raw_affiliation_strings":["School of Management Science, Qufu Normal University","School of Management Science, Qufu Normal University, Rizhao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management Science, Qufu Normal University","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"School of Management Science, Qufu Normal University, Rizhao, People's Republic of China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100377617","display_name":"Yun Wang","orcid":"https://orcid.org/0000-0002-3230-7686"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yun Wang","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University","College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Taian, People's Republic of China","institution_ids":["https://openalex.org/I74485261"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100377617"],"corresponding_institution_ids":["https://openalex.org/I74485261"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09601061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"6","first_page":"2251","last_page":"2272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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":0.9993000030517578,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9948999881744385,"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":0.9930999875068665,"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":0.7343214154243469},{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.7277946472167969},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6709252595901489},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5543708205223083},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.5458134412765503},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5418551564216614},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5076886415481567},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4387192130088806},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41473448276519775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38741689920425415},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3643341660499573},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20193615555763245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14729651808738708},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1229948103427887},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1147303581237793},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06472453474998474}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7343214154243469},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.7277946472167969},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6709252595901489},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5543708205223083},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.5458134412765503},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5418551564216614},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5076886415481567},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4387192130088806},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41473448276519775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38741689920425415},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3643341660499573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20193615555763245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14729651808738708},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1229948103427887},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1147303581237793},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06472453474998474},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2022.2064467","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2022.2064467","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G132072764","display_name":null,"funder_award_id":"11871302,71773067","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W260788981","https://openalex.org/W571616079","https://openalex.org/W593050460","https://openalex.org/W1569098853","https://openalex.org/W1978706921","https://openalex.org/W1984326218","https://openalex.org/W1986000129","https://openalex.org/W1992208280","https://openalex.org/W2006262045","https://openalex.org/W2010043402","https://openalex.org/W2013990204","https://openalex.org/W2061174052","https://openalex.org/W2070589948","https://openalex.org/W2121287494","https://openalex.org/W2142056448","https://openalex.org/W2153083307","https://openalex.org/W2256376045","https://openalex.org/W2413459596","https://openalex.org/W2591355265","https://openalex.org/W2796881136","https://openalex.org/W2947562187","https://openalex.org/W2957358666","https://openalex.org/W2962768795","https://openalex.org/W2963103936","https://openalex.org/W2963569298","https://openalex.org/W2963683203","https://openalex.org/W2964224255","https://openalex.org/W2964312586","https://openalex.org/W2972593485","https://openalex.org/W2995485644","https://openalex.org/W3087441416","https://openalex.org/W3216109598","https://openalex.org/W4285024861"],"related_works":["https://openalex.org/W2571250333","https://openalex.org/W2080619493","https://openalex.org/W2612688603","https://openalex.org/W2337526384","https://openalex.org/W2475071348","https://openalex.org/W2949313682","https://openalex.org/W4292095928","https://openalex.org/W2951095141","https://openalex.org/W4255726860","https://openalex.org/W4388374767"],"abstract_inverted_index":{"In":[0,122],"this":[1],"paper,":[2],"we":[3],"discuss":[4],"the":[5,8,27,40,43,60,63,73,89,101,104,113,120,123,127,137],"isotonicity":[6,41],"of":[7,30,42,62,72,103],"proximity":[9,44,74],"operator":[10,45,75],"in":[11],"Hilbert":[12],"quasi-lattices":[13],"endowed":[14],"with":[15,117],"different":[16,96],"Lorentz":[17,21,56,65],"cones.":[18],"The":[19],"extended":[20,64],"cone":[22],"is":[23],"first":[24],"defined":[25],"by":[26,55,95],"Minkowski":[28],"functionals":[29],"some":[31,36,82],"subsets.":[32],"We":[33],"then":[34],"establish":[35],"sufficient":[37],"conditions":[38,131],"for":[39,88,133],"concerning":[46],"one":[47],"order":[48,97],"and":[49,67,84,112,140],"two":[50],"mutually":[51],"dual":[52],"orders":[53],"induced":[54],"cones,":[57],"respectively.":[58],"Similarly,":[59],"cases":[61],"cones":[66],"other":[68],"ordered":[69],"inequality":[70,130],"properties":[71],"are":[76,93,115,143],"analysed.":[77],"By":[78],"adopting":[79],"these":[80],"characterizations,":[81],"solvability":[83],"iterative":[85],"algorithm":[86],"theorems":[87],"stochastic":[90,124],"optimization":[91],"problem":[92],"established":[94],"approaches.":[98],"For":[99],"solvability,":[100],"gradient":[102],"mappings":[105,128],"does":[106],"not":[107],"need":[108],"to":[109,119],"be":[110],"continuous,":[111],"solutions":[114],"optimal":[116],"respect":[118],"orders.":[121],"proximal":[125],"algorithms,":[126],"satisfy":[129],"just":[132],"comparable":[134],"elements,":[135],"but":[136],"convergence":[138,141],"direction":[139],"rate":[142],"more":[144],"optimal.":[145]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
