{"id":"https://openalex.org/W4412081467","doi":"https://doi.org/10.1109/tac.2025.3586762","title":"Convergence Analysis of Stochastic Saddle Point Mirror Descent Algorithm: A Projected Dynamical Viewpoint","display_name":"Convergence Analysis of Stochastic Saddle Point Mirror Descent Algorithm: A Projected Dynamical Viewpoint","publication_year":2025,"publication_date":"2025-07-07","ids":{"openalex":"https://openalex.org/W4412081467","doi":"https://doi.org/10.1109/tac.2025.3586762"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3586762","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3586762","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic 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/A5088208382","display_name":"Anik Kumar Paul","orcid":"https://orcid.org/0000-0001-6206-5932"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Anik Kumar Paul","raw_affiliation_strings":["Department of Electrical Engineering, IIT Madras, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Madras, Chennai, India","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059111533","display_name":"Arun D. Mahindrakar","orcid":"https://orcid.org/0000-0002-7866-4363"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Arun D Mahindrakar","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025105353","display_name":"Rachel Kalpana Kalaimani","orcid":"https://orcid.org/0000-0002-0701-7927"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rachel Kalpana Kalaimani","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India","institution_ids":["https://openalex.org/I24676775"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088208382"],"corresponding_institution_ids":["https://openalex.org/I24676775"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19958391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"1","first_page":"139","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9811999797821045,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9811999797821045,"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/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.967199981212616,"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/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.9318000078201294,"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/saddle-point","display_name":"Saddle point","score":0.800055980682373},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7063997387886047},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5456295013427734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5349183678627014},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5150489807128906},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5117552280426025},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5095327496528625},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44270285964012146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40792614221572876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33559107780456543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3317359685897827},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14391794800758362},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07947543263435364},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07152551412582397},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06971198320388794}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.800055980682373},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7063997387886047},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5456295013427734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5349183678627014},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5150489807128906},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5117552280426025},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5095327496528625},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44270285964012146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40792614221572876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33559107780456543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3317359685897827},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14391794800758362},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07947543263435364},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07152551412582397},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06971198320388794},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3586762","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3586762","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1486118835","https://openalex.org/W1571174635","https://openalex.org/W1964757264","https://openalex.org/W1971945429","https://openalex.org/W1978259121","https://openalex.org/W2020123437","https://openalex.org/W2037710455","https://openalex.org/W2048723778","https://openalex.org/W2114973703","https://openalex.org/W2149479912","https://openalex.org/W2154056001","https://openalex.org/W2752509387","https://openalex.org/W2912098123","https://openalex.org/W2923133561","https://openalex.org/W2942536919","https://openalex.org/W2962717811","https://openalex.org/W2963331653","https://openalex.org/W2963470657","https://openalex.org/W2963651047","https://openalex.org/W2963910188","https://openalex.org/W2969507060","https://openalex.org/W2978271482","https://openalex.org/W2995729984","https://openalex.org/W3025638325","https://openalex.org/W3083021344","https://openalex.org/W3129263909","https://openalex.org/W4206742934","https://openalex.org/W4252999360","https://openalex.org/W4253214256","https://openalex.org/W4292022450","https://openalex.org/W4323539420","https://openalex.org/W4379409451","https://openalex.org/W4399122064"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W1572705989","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2087062149"],"abstract_inverted_index":{"Saddle":[0,95,133],"point":[1,26,43],"problems,":[2],"ubiquitous":[3],"in":[4,50,155],"optimization,":[5],"extend":[6],"beyond":[7],"game":[8],"theory":[9],"to":[10,23,40,147],"diverse":[11],"domains":[12],"like":[13],"power":[14],"networks":[15],"and":[16,74,79,101],"reinforcement":[17],"learning.":[18],"We":[19],"present":[20,92],"novel":[21],"approaches":[22],"tackle":[24,41],"saddle":[25,42,151],"problem,":[27],"with":[28,105],"a":[29,46,51,65,148],"focus":[30],"on":[31],"continuous-time":[32,108,115],"contexts.":[33],"A":[34],"continuous":[35,86],"time":[36,87],"dynamics":[37],"is":[38],"proposed":[39,85,107],"problem":[44],"utilizing":[45],"projected":[47],"dynamical":[48,88],"system":[49],"non-Euclidean":[52],"domain.":[53],"This":[54],"involves":[55],"computing":[56],"the":[57,61,76,84,93,106,114,119,124,130,162],"(sub/super)":[58],"gradient":[59],"of":[60,83,113,123,176,179],"min-max":[62],"function":[63],"within":[64],"Riemannian":[66],"metric.":[67],"Additionally,":[68],"we":[69,91,117,128],"establish":[70,102],"viable":[71],"Carath\u00e9odory":[72],"solutions":[73],"prove":[75],"Lyapunov":[77],"stability":[78,82,111],"asymptotic":[80],"set":[81],"system.":[89],"Next,":[90],"Stochastic":[94,131],"Point":[96,134],"Mirror":[97,135],"Descent":[98,136],"(SSPMD)":[99],"algorithm":[100],"its":[103],"equivalence":[104],"dynamics.":[109],"Leveraging":[110],"analysis":[112,154,175],"dynamics,":[116],"demonstrate":[118],"almost":[120],"sure":[121],"convergence":[122,146],"algorithm's":[125],"iterates.":[126],"Furthermore,":[127],"introduce":[129],"Zeroth-Order":[132],"(SZSPMD)":[137],"algorithm,":[138],"which":[139],"approximates":[140],"gradients":[141],"using":[142],"Gaussian":[143],"Approximation,":[144],"showcasing":[145],"neighbourhood":[149],"about":[150],"points.":[152],"The":[153],"this":[156],"paper":[157],"provides":[158],"geometric":[159],"insights":[160,170],"into":[161],"mirror":[163,181],"descent":[164,182],"algorithm.":[165,183],"It":[166],"demonstrates":[167],"how":[168],"these":[169],"offer":[171],"theoretical":[172],"foundations":[173],"for":[174],"different":[177],"variants":[178],"stochastic":[180]},"counts_by_year":[],"updated_date":"2025-12-31T23:11:33.660297","created_date":"2025-10-10T00:00:00"}