{"id":"https://openalex.org/W4408410881","doi":"https://doi.org/10.1177/01423312251319586","title":"<i>H</i> <sub>2</sub> optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold","display_name":"<i>H</i> <sub>2</sub> optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold","publication_year":2025,"publication_date":"2025-03-13","ids":{"openalex":"https://openalex.org/W4408410881","doi":"https://doi.org/10.1177/01423312251319586"},"language":"en","primary_location":{"id":"doi:10.1177/01423312251319586","is_oa":false,"landing_page_url":"https://doi.org/10.1177/01423312251319586","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","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/A5018157052","display_name":"Ping Yang","orcid":"https://orcid.org/0000-0002-5443-8193"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]},{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Yang","raw_affiliation_strings":["College of Mathematics and System Science, Xinjiang University, China","School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China"],"raw_orcid":"https://orcid.org/0000-0002-5443-8193","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Science, Xinjiang University, China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101815831","display_name":"Zhaohong Wang","orcid":"https://orcid.org/0000-0002-0185-7765"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhao-Hong Wang","raw_affiliation_strings":["College of Mathematics and System Science, Xinjiang University, China"],"raw_orcid":"https://orcid.org/0000-0002-0185-7765","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Science, Xinjiang University, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034372090","display_name":"Yao\u2010Lin Jiang","orcid":"https://orcid.org/0000-0002-5541-1136"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao-Lin Jiang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China"],"raw_orcid":"https://orcid.org/0000-0002-5541-1136","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101815831"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03588138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"9","first_page":"1667","last_page":"1677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/oblique-case","display_name":"Oblique case","score":0.8279297947883606},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.7222158312797546},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6249455809593201},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5431259870529175},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.5204484462738037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3965516686439514},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3959265351295471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38081270456314087},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3746112585067749},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35226601362228394},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3421822786331177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3130246698856354},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2988455593585968},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1808892786502838},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17942917346954346},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.08648774027824402}],"concepts":[{"id":"https://openalex.org/C160697094","wikidata":"https://www.wikidata.org/wiki/Q1233197","display_name":"Oblique case","level":2,"score":0.8279297947883606},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.7222158312797546},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6249455809593201},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5431259870529175},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.5204484462738037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3965516686439514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3959265351295471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38081270456314087},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3746112585067749},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35226601362228394},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3421822786331177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3130246698856354},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2988455593585968},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1808892786502838},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17942917346954346},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.08648774027824402},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/01423312251319586","is_oa":false,"landing_page_url":"https://doi.org/10.1177/01423312251319586","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3006264087","display_name":null,"funder_award_id":"2022JQ-067","funder_id":"https://openalex.org/F4320336567","funder_display_name":"Natural Science Basic Research Program of Shaanxi Province"},{"id":"https://openalex.org/G3588039652","display_name":null,"funder_award_id":"2023-YBSF-399","funder_id":"https://openalex.org/F4320336350","funder_display_name":"Key Research and Development Projects of Shaanxi Province"},{"id":"https://openalex.org/G4674650358","display_name":null,"funder_award_id":"2023D01C163","funder_id":"https://openalex.org/F4320311028","funder_display_name":"Natural Science Foundation of Xinjiang Province"},{"id":"https://openalex.org/G8763304138","display_name":null,"funder_award_id":"12271426","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311028","display_name":"Natural Science Foundation of Xinjiang Province","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336350","display_name":"Key Research and Development Projects of Shaanxi Province","ror":null},{"id":"https://openalex.org/F4320336567","display_name":"Natural Science Basic Research Program of Shaanxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1551480811","https://openalex.org/W1891861977","https://openalex.org/W1966992674","https://openalex.org/W1996721343","https://openalex.org/W2003772019","https://openalex.org/W2036272365","https://openalex.org/W2056064986","https://openalex.org/W2065313971","https://openalex.org/W2080925234","https://openalex.org/W2088636284","https://openalex.org/W2144326820","https://openalex.org/W2151914729","https://openalex.org/W2152665065","https://openalex.org/W2167623372","https://openalex.org/W2528252365","https://openalex.org/W2909881059","https://openalex.org/W2912249708","https://openalex.org/W2963704853","https://openalex.org/W2965036497","https://openalex.org/W3089788132","https://openalex.org/W3122871637","https://openalex.org/W3130811428","https://openalex.org/W3150565301","https://openalex.org/W3185635697","https://openalex.org/W3202247240","https://openalex.org/W3210315116","https://openalex.org/W4205293427","https://openalex.org/W4225740441","https://openalex.org/W4308624735","https://openalex.org/W4312280737","https://openalex.org/W4362580173","https://openalex.org/W4387350773","https://openalex.org/W4390238595","https://openalex.org/W4394693306","https://openalex.org/W6684641359"],"related_works":["https://openalex.org/W2385104873","https://openalex.org/W2015060724","https://openalex.org/W3001809259","https://openalex.org/W2919324478","https://openalex.org/W2035047702","https://openalex.org/W1600457464","https://openalex.org/W2315802443","https://openalex.org/W2767923834","https://openalex.org/W2376104286","https://openalex.org/W2082353735"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,66,79,93],"the":[4,16,20,23,30,34,44,51,67,80,84,88,94,101,115,124,129,139,142],"H":[5,35,52],"2":[6,36,53],"optimal":[7,37,54],"model":[8,38,55,144],"reduction":[9,39,56,145],"problem":[10,40,57,64,77,91],"of":[11,19,110,118,141],"positive":[12,21],"systems.":[13],"According":[14],"to":[15,106],"coefficient":[17],"matrices":[18],"system,":[22],"nonnegative":[24],"orthonormal":[25,48],"matrix":[26,46],"is":[27,41,47,58,97,133],"taken":[28],"as":[29,60,73],"projection":[31,45],"matrix,":[32],"and":[33,49,70],"developed.":[42],"Since":[43],"nonnegative,":[50],"reformulated":[59],"a":[61,74,108,119],"constrained":[62,75,89],"optimization":[63,76,90,112],"defined":[65,78,92],"Stiefel":[68],"manifold,":[69],"further":[71],"regarded":[72],"oblique":[81,95],"manifold.":[82],"By":[83],"augmented":[85],"Lagrangian":[86],"function,":[87],"manifold":[96],"tackled":[98],"by":[99,128],"employing":[100],"Dai-Yuan-type":[102],"conjugate":[103,130],"gradient":[104,131],"method":[105,132],"solve":[107],"series":[109],"unconstrained":[111],"subproblems.":[113],"When":[114],"objective":[116],"function":[117],"subproblem":[120],"satisfies":[121],"some":[122],"conditions,":[123],"iterative":[125],"sequence":[126],"produced":[127],"convergent.":[134],"Finally,":[135],"numerical":[136],"experiments":[137],"illustrate":[138],"efficiency":[140],"proposed":[143],"method.":[146]},"counts_by_year":[],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
