{"id":"https://openalex.org/W2125062699","doi":"https://doi.org/10.1090/mcom/3178","title":"Penalty methods with stochastic approximation for stochastic nonlinear programming","display_name":"Penalty methods with stochastic approximation for stochastic nonlinear programming","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2125062699","doi":"https://doi.org/10.1090/mcom/3178","mag":"2125062699"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3178","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3178","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5100411516","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0003-2335-8075"},"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/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210096250","display_name":"Beijing Institute of Big Data Research","ror":"https://ror.org/00s1sz824","country_code":"CN","type":"facility","lineage":["https://openalex.org/I20231570","https://openalex.org/I37796252","https://openalex.org/I4210096250"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences; Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, People\u00e2\u0080\u0099s Republic of China","School of Mathematical Sciences, University of Chinese Academy of Sciences","Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences; Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, People's Republic of China","institution_ids":["https://openalex.org/I4210096250","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008787209","display_name":"Shiqian Ma","orcid":"https://orcid.org/0000-0003-1967-1069"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiqian Ma","raw_affiliation_strings":["Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107835542","display_name":"Ya-xiang Yuan","orcid":null},"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/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya-xiang Yuan","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, People\u00e2\u0080\u0099s Republic of China","State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, People\u00e2\u0080\u0099s Republic of 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, People's Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100411516"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210096250","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":1.8684,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.86717731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"86","issue":"306","first_page":"1793","last_page":"1820"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983999729156494,"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":0.9970999956130981,"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/oracle","display_name":"Oracle","score":0.7016068696975708},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6821690201759338},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.681078314781189},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6394878625869751},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.6194798350334167},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6024120450019836},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.5995396375656128},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5511224269866943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49663692712783813},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4389401972293854},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4230273365974426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22349655628204346},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.06432795524597168}],"concepts":[{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7016068696975708},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6821690201759338},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.681078314781189},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6394878625869751},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.6194798350334167},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6024120450019836},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.5995396375656128},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5511224269866943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49663692712783813},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4389401972293854},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4230273365974426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22349655628204346},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.06432795524597168},{"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/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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:10.1090/mcom/3178","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3178","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.75,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W29692742","https://openalex.org/W1505731132","https://openalex.org/W1541527977","https://openalex.org/W1569990960","https://openalex.org/W1583412610","https://openalex.org/W1852945463","https://openalex.org/W1972711404","https://openalex.org/W1975768153","https://openalex.org/W1983916623","https://openalex.org/W1987083649","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W1995033525","https://openalex.org/W1995126983","https://openalex.org/W1995878217","https://openalex.org/W2004357692","https://openalex.org/W2005876975","https://openalex.org/W2019465316","https://openalex.org/W2020929673","https://openalex.org/W2024484010","https://openalex.org/W2029463628","https://openalex.org/W2045744861","https://openalex.org/W2048923650","https://openalex.org/W2086161653","https://openalex.org/W2092679899","https://openalex.org/W2122203560","https://openalex.org/W2122587727","https://openalex.org/W2128038973","https://openalex.org/W2149479912","https://openalex.org/W2162746441","https://openalex.org/W2166365115","https://openalex.org/W2168909589","https://openalex.org/W2181317554","https://openalex.org/W2237681562","https://openalex.org/W2295489065","https://openalex.org/W2936995161","https://openalex.org/W2962720772","https://openalex.org/W2963470657","https://openalex.org/W2969945254","https://openalex.org/W3029645440","https://openalex.org/W3100353959","https://openalex.org/W3125612732"],"related_works":["https://openalex.org/W2377522634","https://openalex.org/W4254717236","https://openalex.org/W2377757044","https://openalex.org/W2367437354","https://openalex.org/W3160952126","https://openalex.org/W2362627879","https://openalex.org/W2374291142","https://openalex.org/W2016611441","https://openalex.org/W2281909915","https://openalex.org/W2950466654"],"abstract_inverted_index":{"In":[0,43],"this":[1,76],"paper,":[2],"we":[3,50],"propose":[4],"a":[5,37],"class":[6],"of":[7,28,46,82],"penalty":[8,54,94],"methods":[9,95],"with":[10,61],"stochastic":[11,15,38,63,86],"approximation":[12,70],"for":[13,74,91,96],"solving":[14,75],"nonlinear":[16],"programming":[17],"problems.":[18],"We":[19],"assume":[20],"that":[21],"only":[22,62],"noisy":[23],"gradients":[24],"or":[25,40,65],"function":[26,31,55],"values":[27],"the":[29,47,85,92],"objective":[30],"are":[32,72],"available":[33],"via":[34],"calls":[35,83],"to":[36,84],"first-order":[39,64,87],"zeroth-order":[41,66],"oracle.":[42],"each":[44],"iteration":[45],"proposed":[48,93],"methods,":[49],"minimize":[51],"an":[52,98],"exact":[53],"which":[56],"is":[57,102],"nonsmooth":[58],"and":[59],"nonconvex":[60],"information":[67],"available.":[68],"Stochastic":[69],"algorithms":[71],"presented":[73],"particular":[77],"subproblem.":[78],"The":[79],"worst-case":[80],"complexity":[81],"(or":[88],"zeroth-order)":[89],"oracle":[90],"obtaining":[97],"$\\epsilon$-stochastic":[99],"critical":[100],"point":[101],"analyzed.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}
