{"id":"https://openalex.org/W7215101571","doi":"https://doi.org/10.48550/arxiv.2609.39240","title":"Boundary Geometry and Global Rates of Cyclic Coordinate Descent for SVM Duals","display_name":"Boundary Geometry and Global Rates of Cyclic Coordinate Descent for SVM Duals","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215101571","doi":"https://doi.org/10.48550/arxiv.2609.39240"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.39240","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39240","pdf_url":"https://arxiv.org/pdf/2609.39240","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.39240","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026215052","display_name":"Egor Leonidovich Gladin","orcid":"https://orcid.org/0000-0002-9086-996X","observed_orcids":["https://orcid.org/0000-0002-9086-996X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gladin, Egor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153871153","display_name":"Eva Ibodova","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ibodova, Eva","raw_affiliation_strings":["HSE University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HSE University","institution_ids":["https://openalex.org/I118501908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9916999936103821,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9916999936103821,"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":0.005400000140070915,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.001500000013038516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cyclic-coordinate-descent","display_name":"cyclic coordinate descent","score":0.9980000257492065},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"support vector machine","score":0.9760000109672546},{"id":"https://openalex.org/keywords/global-linear-convergence","display_name":"global linear convergence","score":0.6389999985694885},{"id":"https://openalex.org/keywords/boundary-geometry","display_name":"boundary geometry","score":0.7770000100135803},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.7730000019073486},{"id":"https://openalex.org/keywords/singular-hessian","display_name":"singular Hessian","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7516000270843506},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6013000011444092},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5672000050544739},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49779999256134033},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3635999858379364},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3377000093460083},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32499998807907104},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3151000142097473},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3075000047683716},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28360000252723694},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.39240","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39240","pdf_url":"https://arxiv.org/pdf/2609.39240","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.39240","doi":"https://doi.org/10.48550/arxiv.2609.39240","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.39240","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.39240","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39240","pdf_url":"https://arxiv.org/pdf/2609.39240","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215101571.pdf","grobid_xml":"https://content.openalex.org/works/W7215101571.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1600762120","https://openalex.org/W1979896658","https://openalex.org/W1994433358","https://openalex.org/W2090084467","https://openalex.org/W2101868363","https://openalex.org/W2153635508","https://openalex.org/W2165966284","https://openalex.org/W2249945205","https://openalex.org/W2278798990","https://openalex.org/W2504151877","https://openalex.org/W2951335402","https://openalex.org/W2979298859","https://openalex.org/W3002526051","https://openalex.org/W3035235874","https://openalex.org/W3094244489","https://openalex.org/W4414425471"],"related_works":["https://openalex.org/W4385451997","https://openalex.org/W2117669906","https://openalex.org/W2085650911","https://openalex.org/W7098067042","https://openalex.org/W7100344620","https://openalex.org/W2789819709","https://openalex.org/W4384575246","https://openalex.org/W2597892042","https://openalex.org/W2809196974","https://openalex.org/W3190432243"],"abstract_inverted_index":{"Cyclic":[0],"coordinate":[1,30,44,58],"descent":[2],"is":[3,176],"widely":[4],"used":[5],"to":[6],"train":[7],"support":[8],"vector":[9],"machines,":[10],"but":[11],"global":[12,38,133],"linear":[13],"convergence":[14,50],"alone":[15],"gives":[16],"limited":[17],"guidance":[18],"about":[19],"the":[20,62,66,79,96,106,112,117,120,124,148,183],"rate":[21],"on":[22,78,186,192],"a":[23,74,132,155,159],"particular":[24],"instance.":[25],"We":[26,145],"study":[27],"exact":[28],"cyclic":[29],"minimization":[31],"for":[32,85,141,181],"box-constrained":[33],"convex":[34],"quadratics":[35],"and":[36,46,69,92,189],"develop":[37],"contraction":[39,126,166,185],"bounds":[40,152],"that":[41,123],"capture":[42],"both":[43,110],"order":[45],"boundary":[47,171],"geometry.":[48],"Our":[49],"certificate":[51],"combines":[52],"two":[53],"ingredients:":[54],"interactions":[55],"between":[56],"successive":[57],"updates,":[59],"encoded":[60],"by":[61,73,153,178],"triangular":[63],"part":[64],"of":[65,101,127,150],"normalized":[67,162],"Hessian,":[68,163],"objective":[70],"growth,":[71],"captured":[72],"matrix":[75],"lower":[76],"bound":[77,135],"optimality":[80],"gap.":[81],"It":[82],"remains":[83,131],"valid":[84],"cases":[86],"with":[87,139,158],"singular":[88,161],"Hessians,":[89],"nonunique":[90],"minimizers,":[91],"updates":[93],"clipped":[94],"at":[95],"boundary.":[97],"An":[98],"error-bound":[99,114],"specialization":[100],"our":[102],"analysis":[103,121],"strictly":[104],"sharpens":[105],"Wang-Lin":[107],"factor":[108],"when":[109],"use":[111],"same":[113],"constant.":[115],"In":[116],"positive-definite":[118],"case,":[119],"shows":[122],"worst-case":[125,165,184],"one":[128,168],"Gauss-Seidel":[129],"sweep":[130],"upper":[134],"under":[136],"box":[137],"constraints,":[138],"equality":[140],"an":[142],"interior":[143],"optimizer.":[144],"also":[146],"demonstrate":[147],"limitations":[149],"Hessian-only":[151],"constructing":[154],"two-coordinate":[156],"family":[157],"fixed":[160],"whose":[164],"approaches":[167],"as":[169],"its":[170],"margin":[172],"vanishes.":[173],"The":[174],"theory":[175],"complemented":[177],"practical":[179],"procedures":[180],"bounding":[182],"individual":[187],"instances":[188],"numerical":[190],"evaluation":[191],"several":[193],"classical":[194],"SVM":[195],"datasets.":[196]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-02T00:00:00"}
