{"id":"https://openalex.org/W2883328360","doi":"https://doi.org/10.1080/10556788.2019.1571590","title":"The method of codifferential descent for convex and global piecewise affine optimization","display_name":"The method of codifferential descent for convex and global piecewise affine optimization","publication_year":2019,"publication_date":"2019-02-04","ids":{"openalex":"https://openalex.org/W2883328360","doi":"https://doi.org/10.1080/10556788.2019.1571590","mag":"2883328360"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2019.1571590","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1571590","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.05538","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000808861","display_name":"\u041c. \u0412. \u0414\u043e\u043b\u0433\u043e\u043f\u043e\u043b\u0438\u043a","orcid":"https://orcid.org/0000-0003-0677-0797"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I4210142628","display_name":"Institute of Problems of Mechanical Engineering","ror":"https://ror.org/047pt5178","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210142628","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"M. V. Dolgopolik","raw_affiliation_strings":["Institute for Problems in Mechanical Engineering RAS, Saint Petersburg, Russia","Saint Petersburg State University, Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0003-0677-0797","affiliations":[{"raw_affiliation_string":"Institute for Problems in Mechanical Engineering RAS, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210142628"]},{"raw_affiliation_string":"Saint Petersburg State University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000808861"],"corresponding_institution_ids":["https://openalex.org/I172901346","https://openalex.org/I4210142628"],"apc_list":null,"apc_paid":null,"fwci":1.4761,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7917758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"35","issue":"6","first_page":"1191","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9926000237464905,"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/mathematics","display_name":"Mathematics","score":0.8241536617279053},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7410991191864014},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6255127191543579},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5982956886291504},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.555442750453949},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5488484501838684},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.49262911081314087},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4711315333843231},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45391279458999634},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.43604832887649536},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4281392991542816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42043066024780273},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.41666150093078613},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.41025111079216003},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1905621588230133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15144792199134827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13844233751296997},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06302189826965332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8241536617279053},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7410991191864014},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6255127191543579},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5982956886291504},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.555442750453949},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5488484501838684},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.49262911081314087},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4711315333843231},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45391279458999634},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.43604832887649536},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4281392991542816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42043066024780273},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.41666150093078613},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.41025111079216003},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1905621588230133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15144792199134827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13844233751296997},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06302189826965332},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556788.2019.1571590","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1571590","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.05538","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.05538","pdf_url":"https://arxiv.org/pdf/1807.05538","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,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.05538","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.05538","pdf_url":"https://arxiv.org/pdf/1807.05538","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,"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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G4761510440","display_name":null,"funder_award_id":"18-31-00014","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W27416461","https://openalex.org/W53341510","https://openalex.org/W205831359","https://openalex.org/W585047121","https://openalex.org/W1516695992","https://openalex.org/W1524477546","https://openalex.org/W1553702074","https://openalex.org/W1597196612","https://openalex.org/W1653619892","https://openalex.org/W1863473538","https://openalex.org/W1985240368","https://openalex.org/W1989304426","https://openalex.org/W1995460185","https://openalex.org/W1996833224","https://openalex.org/W1999130931","https://openalex.org/W2001324813","https://openalex.org/W2013604529","https://openalex.org/W2022150446","https://openalex.org/W2029282549","https://openalex.org/W2030161963","https://openalex.org/W2034687848","https://openalex.org/W2048283847","https://openalex.org/W2068889684","https://openalex.org/W2083029110","https://openalex.org/W2084704795","https://openalex.org/W2089472568","https://openalex.org/W2124541940","https://openalex.org/W2143013250","https://openalex.org/W2167732364","https://openalex.org/W2175532135","https://openalex.org/W2182529896","https://openalex.org/W2189016032","https://openalex.org/W2606743926","https://openalex.org/W2784408805","https://openalex.org/W2912349752","https://openalex.org/W2915749893","https://openalex.org/W2964347994","https://openalex.org/W2979409118","https://openalex.org/W3151826485","https://openalex.org/W4206570602","https://openalex.org/W4241137470","https://openalex.org/W4247489173","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W3080334989","https://openalex.org/W2088448568","https://openalex.org/W2015288657","https://openalex.org/W4226095963","https://openalex.org/W2366552965","https://openalex.org/W2372778757","https://openalex.org/W4377090276","https://openalex.org/W2364567920","https://openalex.org/W1994778783","https://openalex.org/W2740262376"],"abstract_inverted_index":{"The":[0],"class":[1,73],"of":[2,28,42,48,58,65,68,74,93,114,129,134,141,152,166,197,200,210],"nonsmooth":[3,49,75],"codifferentiable":[4],"functions":[5,24,77,126,148,169],"was":[6],"introduced":[7],"by":[8],"professor":[9],"V.F.":[10],"Demyanov":[11],"in":[12,83,99,127,191,206],"the":[13,26,40,55,59,63,66,84,90,94,102,105,111,115,132,142,150,167,176,183,192],"late":[14],"1980s.":[15],"He":[16],"also":[17],"proposed":[18,190],"a":[19,72,139,195,201,207],"method":[20,27,44,67,151],"for":[21,123,144,175],"minimizing":[22,145],"these":[23,135],"called":[25],"codifferential":[29,69,154],"descent":[30,70],"(MCD).":[31],"However,":[32],"until":[33],"now":[34],"almost":[35],"no":[36,172],"theoretical":[37],"results":[38],"on":[39,45,71],"performance":[41,64],"this":[43,100],"particular":[46],"classes":[47],"optimization":[50,177],"problems":[51],"were":[52],"known.":[53],"In":[54,110],"first":[56],"part":[57,113],"paper,":[60],"we":[61,117,137,180],"study":[62],"convex":[76],"satisfying":[78],"some":[79],"regularity":[80],"assumptions,":[81],"which":[82],"smooth":[85],"case":[86,101],"are":[87,171],"reduced":[88],"to":[89],"Lipschitz":[91],"continuity":[92],"gradient.":[95],"We":[96],"prove":[97,181],"that":[98,156,170,182],"MCD":[103,143,184],"has":[104],"iteration":[106],"complexity":[107],"bound":[108],"O(1/\u03b5).":[109],"second":[112],"paper":[116],"obtain":[118],"new":[119],"global":[120,153,198],"optimality":[121],"conditions":[122,136],"piecewise":[124,146,203],"affine":[125,147,204],"terms":[128],"codifferentials.":[130],"With":[131],"use":[133,159],"propose":[138],"modification":[140,189],"(called":[149],"descent)":[155],"does":[157],"not":[158],"line":[160],"search,":[161],"and":[162],"discards":[163],"those":[164],"\u2018pieces\u2019":[165],"objective":[168],"longer":[173],"useful":[174],"process.":[178],"Then":[179],"as":[185,187],"well":[186],"its":[188],"article":[193],"find":[194],"point":[196],"minimum":[199],"nonconvex":[202],"function":[205],"finite":[208],"number":[209],"steps.":[211]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}