{"id":"https://openalex.org/W3042629719","doi":"https://doi.org/10.1007/s10107-020-01538-6","title":"Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs","display_name":"Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs","publication_year":2020,"publication_date":"2020-07-14","ids":{"openalex":"https://openalex.org/W3042629719","doi":"https://doi.org/10.1007/s10107-020-01538-6","mag":"3042629719"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01538-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01538-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01538-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01538-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042104231","display_name":"Hernan Le\u00f6vey","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163805","display_name":"Axpo (Switzerland)","ror":"https://ror.org/05frtgg14","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210163805"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"H. Le\u00f6vey","raw_affiliation_strings":["Structured Energy Management Team, Axpo, Baden, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Structured Energy Management Team, Axpo, Baden, Switzerland","institution_ids":["https://openalex.org/I4210163805"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087450694","display_name":"Werner R\u00f6misch","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. R\u00f6misch","raw_affiliation_strings":["Institute of Mathematics, Humboldt-University Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3853-5257","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Humboldt-University Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087450694"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.2956,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51319444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"190","issue":"1-2","first_page":"361","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9995999932289124,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9995999932289124,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8392362594604492},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6274843215942383},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6049432754516602},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5394597053527832},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5070154666900635},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5044270753860474},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.47205883264541626},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.46543779969215393},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.44687843322753906},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4279828667640686},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40545380115509033},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2956988215446472},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23679310083389282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06517517566680908},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06313097476959229}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8392362594604492},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6274843215942383},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6049432754516602},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5394597053527832},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5070154666900635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044270753860474},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.47205883264541626},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.46543779969215393},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.44687843322753906},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4279828667640686},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40545380115509033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2956988215446472},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23679310083389282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06517517566680908},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06313097476959229},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-020-01538-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01538-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01538-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:edoc.hu-berlin.de:18452/24657","is_oa":true,"landing_page_url":"http://edoc.hu-berlin.de/18452/24657","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10107-020-01538-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01538-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01538-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323700","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3042629719.pdf","grobid_xml":"https://content.openalex.org/works/W3042629719.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W206670954","https://openalex.org/W229300124","https://openalex.org/W290023117","https://openalex.org/W598051755","https://openalex.org/W1493969319","https://openalex.org/W1511560458","https://openalex.org/W1513869646","https://openalex.org/W1533955387","https://openalex.org/W1539454454","https://openalex.org/W1565176583","https://openalex.org/W1593038947","https://openalex.org/W1593981206","https://openalex.org/W1597196612","https://openalex.org/W1602210307","https://openalex.org/W1602773783","https://openalex.org/W1618463987","https://openalex.org/W1788645602","https://openalex.org/W1825668880","https://openalex.org/W1965440168","https://openalex.org/W1971209264","https://openalex.org/W1971362449","https://openalex.org/W1978501336","https://openalex.org/W1983916623","https://openalex.org/W1986280275","https://openalex.org/W1995565517","https://openalex.org/W1998160729","https://openalex.org/W2002274796","https://openalex.org/W2004971474","https://openalex.org/W2011200438","https://openalex.org/W2012865252","https://openalex.org/W2014641274","https://openalex.org/W2016770622","https://openalex.org/W2019441776","https://openalex.org/W2024626809","https://openalex.org/W2032320685","https://openalex.org/W2033560593","https://openalex.org/W2042083287","https://openalex.org/W2054110366","https://openalex.org/W2059141990","https://openalex.org/W2065021724","https://openalex.org/W2065230098","https://openalex.org/W2070058271","https://openalex.org/W2077499284","https://openalex.org/W2080288600","https://openalex.org/W2093625674","https://openalex.org/W2095595785","https://openalex.org/W2100179204","https://openalex.org/W2101589741","https://openalex.org/W2113753459","https://openalex.org/W2117784255","https://openalex.org/W2124189866","https://openalex.org/W2132851968","https://openalex.org/W2228579993","https://openalex.org/W2328523441","https://openalex.org/W2963354045","https://openalex.org/W2963818518","https://openalex.org/W3017463949","https://openalex.org/W3021737829","https://openalex.org/W4206570602","https://openalex.org/W4234552994","https://openalex.org/W4245807314","https://openalex.org/W4248381180","https://openalex.org/W4251442645"],"related_works":["https://openalex.org/W1972096828","https://openalex.org/W2529137940","https://openalex.org/W4302048708","https://openalex.org/W2359913921","https://openalex.org/W4239740410","https://openalex.org/W1996195943","https://openalex.org/W4205298958","https://openalex.org/W1981385315","https://openalex.org/W2953303953","https://openalex.org/W4287117439"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"randomized":[3,96],"QMC":[4,97],"methods":[5,98],"for":[6],"approximating":[7],"the":[8,20,27,41,63,87,100],"expected":[9],"recourse":[10],"in":[11,19],"two-stage":[12],"stochastic":[13],"optimization":[14],"problems":[15],"containing":[16],"mixed-integer":[17],"decisions":[18],"second":[21],"stage.":[22],"It":[23],"is":[24,32,50,104],"known":[25],"that":[26,56],"second-stage":[28],"optimal":[29],"value":[30],"function":[31],"piecewise":[33],"linear-quadratic":[34],"with":[35],"possible":[36],"kinks":[37],"and":[38,58],"discontinuities":[39],"at":[40],"boundaries":[42],"of":[43,62,86,95],"certain":[44],"convex":[45],"polyhedral":[46],"sets.":[47],"This":[48,79],"structure":[49],"exploited":[51],"to":[52,81,91],"provide":[53],"conditions":[54],"implying":[55],"first":[57,75],"higher":[59],"order":[60,76],"terms":[61],"integrand\u2019s":[64],"ANOVA":[65],"decomposition":[66],"(Math.":[67],"Comp.":[68],"79":[69],"(2010),":[70],"953\u2013966)":[71],"have":[72],"mixed":[73],"weak":[74],"partial":[77],"derivatives.":[78],"leads":[80],"a":[82],"good":[83,92],"smooth":[84],"approximation":[85],"integrand":[88],"and,":[89],"hence,":[90],"convergence":[93],"rates":[94],"if":[99],"effective":[101],"(superposition)":[102],"dimension":[103],"low.":[105]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
