{"id":"https://openalex.org/W1579576445","doi":"https://doi.org/10.1137/140964795","title":"Iteration Complexity of a Block Coordinate Gradient Descent Method for Convex Optimization","display_name":"Iteration Complexity of a Block Coordinate Gradient Descent Method for Convex Optimization","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1579576445","doi":"https://doi.org/10.1137/140964795","mag":"1579576445"},"language":"en","primary_location":{"id":"doi:10.1137/140964795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140964795","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5073153795","display_name":"Xiaoqin Hua","orcid":"https://orcid.org/0000-0002-0713-9131"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoqin Hua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109115371","display_name":"Nobuo Yamashita","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nobuo Yamashita","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3232,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.58860318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"3","first_page":"1298","last_page":"1313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976999759674072,"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":0.8422565460205078},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8392037153244019},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6015158295631409},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5778164267539978},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5609252452850342},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5588880181312561},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5404040217399597},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5355678796768188},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5325385928153992},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.4919531047344208},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47543051838874817},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.4127744734287262},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3223995268344879},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3223364055156708},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2796667218208313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2570577561855316},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12497901916503906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07083696126937866}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8422565460205078},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8392037153244019},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6015158295631409},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5778164267539978},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5609252452850342},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5588880181312561},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5404040217399597},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5355678796768188},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5325385928153992},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.4919531047344208},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47543051838874817},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.4127744734287262},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3223995268344879},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3223364055156708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2796667218208313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2570577561855316},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12497901916503906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07083696126937866},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140964795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140964795","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G171157626","display_name":"Study on iteration complexities of proximal coordinate descent methods for the convex optimizaiton","funder_award_id":"25330025","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W137628093","https://openalex.org/W1540764732","https://openalex.org/W1755117326","https://openalex.org/W1974524469","https://openalex.org/W2023901033","https://openalex.org/W2039050532","https://openalex.org/W2075660001","https://openalex.org/W2079482358","https://openalex.org/W2095984592","https://openalex.org/W2101868363","https://openalex.org/W2106398669","https://openalex.org/W2117575248","https://openalex.org/W2117669906","https://openalex.org/W2117686388","https://openalex.org/W2138019504","https://openalex.org/W2950663096"],"related_works":["https://openalex.org/W4288346661","https://openalex.org/W2947416323","https://openalex.org/W4385644471","https://openalex.org/W2811217697","https://openalex.org/W4295266778","https://openalex.org/W4320495396","https://openalex.org/W2768047954","https://openalex.org/W4313177131","https://openalex.org/W2037966176","https://openalex.org/W2804400349"],"abstract_inverted_index":{"In":[0,77],"this":[1],"paper,":[2],"we":[3,79],"study":[4],"the":[5,35,39,52,55,60,65,68,74,81,91,99],"iteration":[6,36],"complexity":[7,37],"of":[8,67,101],"a":[9,17,27],"block":[10],"coordinate":[11],"gradient":[12,66],"descent":[13],"(BCGD)":[14],"method":[15,42],"with":[16],"cyclic":[18],"rule":[19],"for":[20,38,64],"solving":[21],"convex":[22],"optimization":[23],"problems.":[24],"We":[25],"propose":[26],"new":[28],"Lipschitz":[29,62],"continuity-like":[30],"assumption":[31],"and":[32,71,85,87],"show":[33],"that":[34],"proposed":[40,56],"BCGD":[41],"can":[43],"be":[44],"improved":[45],"to":[46],"$O(\\frac{\\max\\{M,":[47],"\\;{L}\\}}{\\varepsilon})$,":[48],"where":[49,96],"$M$":[50,84],"is":[51,59,73,98],"constant":[53,63],"in":[54,90],"assumption,":[57],"${L}$":[58],"usual":[61],"objective":[69],"function,":[70],"$\\varepsilon>0$":[72],"required":[75],"precision.":[76],"addition,":[78],"analyze":[80],"relation":[82],"between":[83],"${L}$,":[86],"prove":[88],"that,":[89],"worst":[92],"case,":[93],"$M\\leq":[94],"\\sqrt{N}{L}$,":[95],"$N$":[97],"number":[100],"blocks.":[102]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}