{"id":"https://openalex.org/W4391020675","doi":"https://doi.org/10.1109/cdc49753.2023.10383237","title":"Smoothing Gradient Tracking for Decentralized Optimization over the Stiefel Manifold with Non-Smooth Regularizers","display_name":"Smoothing Gradient Tracking for Decentralized Optimization over the Stiefel Manifold with Non-Smooth Regularizers","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391020675","doi":"https://doi.org/10.1109/cdc49753.2023.10383237"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383237","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5100436071","display_name":"Lei Wang","orcid":"https://orcid.org/0000-0003-0651-6262"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei Wang","raw_affiliation_strings":["Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences,State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,Beijing,China","State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences,State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,Beijing,China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100352246","display_name":"Xin Liu","orcid":"https://orcid.org/0000-0002-5705-0805"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Liu","raw_affiliation_strings":["Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences,State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,Beijing,China","State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences,State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,Beijing,China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100436071"],"corresponding_institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.4331,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58785896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"126","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/stiefel-manifold","display_name":"Stiefel manifold","score":0.9347331523895264},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7179339528083801},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6654829382896423},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6170782446861267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5126949548721313},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5012505054473877},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4892292022705078},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4861030578613281},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46186524629592896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3636665344238281},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.328008770942688},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15188881754875183},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07444891333580017}],"concepts":[{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.9347331523895264},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7179339528083801},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6654829382896423},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6170782446861267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5126949548721313},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5012505054473877},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4892292022705078},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4861030578613281},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46186524629592896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3636665344238281},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.328008770942688},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15188881754875183},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07444891333580017},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383237","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1571416372","https://openalex.org/W1616857247","https://openalex.org/W1953936588","https://openalex.org/W1979112316","https://openalex.org/W2098000549","https://openalex.org/W2113600901","https://openalex.org/W2220473304","https://openalex.org/W2759764766","https://openalex.org/W2891189546","https://openalex.org/W2913668833","https://openalex.org/W2962771678","https://openalex.org/W2970070132","https://openalex.org/W2999695911","https://openalex.org/W3007623561","https://openalex.org/W3123332075","https://openalex.org/W3129118870","https://openalex.org/W3133689119","https://openalex.org/W3150868911","https://openalex.org/W3156912318","https://openalex.org/W3170923639","https://openalex.org/W3176493728","https://openalex.org/W3198590018","https://openalex.org/W3214820890","https://openalex.org/W4205293427","https://openalex.org/W4226090532","https://openalex.org/W4249513058","https://openalex.org/W4321795558","https://openalex.org/W4327989705","https://openalex.org/W4353007138","https://openalex.org/W4402540349","https://openalex.org/W6754555501","https://openalex.org/W6767359440","https://openalex.org/W6787300317","https://openalex.org/W6789219511","https://openalex.org/W6791727645","https://openalex.org/W6794426080","https://openalex.org/W6796327469","https://openalex.org/W6849618711","https://openalex.org/W6850550873","https://openalex.org/W6850634089","https://openalex.org/W6862553414"],"related_works":["https://openalex.org/W2126146080","https://openalex.org/W2897990660","https://openalex.org/W3025932934","https://openalex.org/W1978572805","https://openalex.org/W2383807498","https://openalex.org/W8105021","https://openalex.org/W2084640076","https://openalex.org/W46024256","https://openalex.org/W183393176","https://openalex.org/W2132884359"],"abstract_inverted_index":{"Recently,":[0],"decentralized":[1,58,112],"optimization":[2,62,85],"over":[3,63],"the":[4,25,35,49,56,69,91,95,111,115],"Stiefel":[5,64],"manifold":[6],"has":[7],"attracted":[8],"tremendous":[9],"attentions":[10],"due":[11],"to":[12,27,34,48],"its":[13,76],"wide":[14],"range":[15],"of":[16,51,72,98,119],"applications":[17],"in":[18],"various":[19],"fields.":[20],"Existing":[21],"methods":[22],"rely":[23],"on":[24],"gradients":[26],"update":[28],"variables,":[29],"which":[30],"are":[31],"not":[32],"applicable":[33],"objective":[36,73],"functions":[37],"with":[38,94],"non-smooth":[39,61,70],"regularizers,":[40],"such":[41],"as":[42],"sparse":[43],"PCA.":[44],"In":[45],"this":[46],"paper,":[47],"best":[50],"our":[52,120],"knowledge,":[53],"we":[54],"propose":[55],"first":[57],"algorithm":[59,67],"for":[60,83],"manifolds.":[65],"Our":[66],"approximates":[68],"part":[71],"function":[74],"by":[75],"Moreau":[77],"envelope,":[78],"and":[79,117],"then":[80],"existing":[81],"algorithms":[82],"smooth":[84],"can":[86],"be":[87],"deployed.":[88],"We":[89],"establish":[90],"convergence":[92],"guarantee":[93],"iteration":[96],"complexity":[97],"<tex":[99],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[100,104],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathcal{O}$</tex>":[101],"(\u220a":[102],"<sup":[103],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sup>":[105],").":[106],"Numerical":[107],"experiments":[108],"conducted":[109],"under":[110],"setting":[113],"demonstrate":[114],"effectiveness":[116],"efficiency":[118],"algorithm.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
