{"id":"https://openalex.org/W1977433610","doi":"https://doi.org/10.1007/bf02031698","title":"Continuous approximation schemes for stochastic programs","display_name":"Continuous approximation schemes for stochastic programs","publication_year":1995,"publication_date":"1995-12-01","ids":{"openalex":"https://openalex.org/W1977433610","doi":"https://doi.org/10.1007/bf02031698","mag":"1977433610"},"language":"en","primary_location":{"id":"doi:10.1007/bf02031698","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02031698","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/2027.42/3655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031580225","display_name":"John R. Birge","orcid":"https://orcid.org/0000-0002-7446-0953"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John R. Birge","raw_affiliation_strings":["Department of Industrial and Operations Engineering, University of Michigan, 48109, Ann Arbor, MI, USA","[Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Operations Engineering, University of Michigan, 48109, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"[Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA]","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["School of Mathematics, The University of New South Wales, 2033, Kensington, N.S.W., Australia","School of Mathematics, the University of New South Wales, Kensington, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, 2033, Kensington, N.S.W., Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, the University of New South Wales, Kensington, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031580225"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6471,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66885074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"1","first_page":"15","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.996999979019165,"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":0.996999979019165,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T12137","display_name":"Economic theories and models","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.7264434099197388},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7204133868217468},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6034852862358093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5847440958023071},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5644919276237488},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5064340829849243},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5017971992492676},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4550815522670746},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4334167540073395},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.4220835268497467},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4219144284725189},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.4174294173717499},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39982926845550537},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.36906546354293823},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.27243417501449585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25905370712280273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1545364260673523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1091093122959137}],"concepts":[{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.7264434099197388},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7204133868217468},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6034852862358093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5847440958023071},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5644919276237488},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5064340829849243},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5017971992492676},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4550815522670746},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4334167540073395},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.4220835268497467},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4219144284725189},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.4174294173717499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39982926845550537},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.36906546354293823},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27243417501449585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25905370712280273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1545364260673523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1091093122959137},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bf02031698","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02031698","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/3655","is_oa":true,"landing_page_url":"https://hdl.handle.net/2027.42/3655","pdf_url":"https://hdl.handle.net/2027.42/3655","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Technical Report"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/44240","is_oa":true,"landing_page_url":"http://hdl.handle.net/2027.42/44240>","pdf_url":"https://hdl.handle.net/2027.42/44240","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Article"}],"best_oa_location":{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/3655","is_oa":true,"landing_page_url":"https://hdl.handle.net/2027.42/3655","pdf_url":"https://hdl.handle.net/2027.42/3655","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Technical Report"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3306165138","display_name":"Computational and Applied Aspects of Multiperiod Stochastic Programming","funder_award_id":"8815101","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5624684463","display_name":"Computational and Applied Aspects of Multiperiod Stochastic Programming","funder_award_id":"9215921","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1977433610.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W55939935","https://openalex.org/W64605562","https://openalex.org/W175440523","https://openalex.org/W377600200","https://openalex.org/W1496506618","https://openalex.org/W1536391780","https://openalex.org/W1551360398","https://openalex.org/W1738394416","https://openalex.org/W1990682629","https://openalex.org/W1994166982","https://openalex.org/W1995033525","https://openalex.org/W1996289149","https://openalex.org/W2007576462","https://openalex.org/W2031756167","https://openalex.org/W2032125776","https://openalex.org/W2033793554","https://openalex.org/W2040104067","https://openalex.org/W2040358553","https://openalex.org/W2042763219","https://openalex.org/W2048225885","https://openalex.org/W2083661799","https://openalex.org/W2116337907","https://openalex.org/W2118152326","https://openalex.org/W2132388847","https://openalex.org/W2133282089","https://openalex.org/W2312972856","https://openalex.org/W2477907299","https://openalex.org/W2491598486","https://openalex.org/W2498029103","https://openalex.org/W4242081728","https://openalex.org/W4298380944"],"related_works":["https://openalex.org/W4286899070","https://openalex.org/W4323366756","https://openalex.org/W2124181538","https://openalex.org/W2734989445","https://openalex.org/W3207830353","https://openalex.org/W3012647659","https://openalex.org/W2067923842","https://openalex.org/W3109737792","https://openalex.org/W4388688818","https://openalex.org/W4386559766"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}