Complexity of stochastic dual dynamic programming

Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Mathematical programming Ročník 191; číslo 2; s. 717 - 754
Hlavný autor:	Lan, Guanghui
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022 Springer Springer Nature B.V
Predmet:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Complexity Decision making Dynamic programming Flying-machines Full Length Paper Iterative methods Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimal control Optimization Stochastic processes Theoretical 90C06 93A14 90C15 49M37 90C25 90C22
ISSN:	0025-5610, 1436-4646
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dual dynamic programming method for solving single-scenario multi-stage optimization problems, by introducing novel mathematical tools including the saturation of search points. We then refine these basic tools and establish the iteration complexity for an explorative dual dynamic programing method proposed herein and the classic stochastic dual dynamic programming method for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption. Our results indicate that the complexity of these methods mildly increases with the number of stages T , in fact linearly dependent on T for discounted problems. Therefore, they are efficient for strategic decision making which involves a large number of stages, but with a relatively small number of decision variables in each stage. Without explicitly discretizing the state and action spaces, these methods might also be pertinent to the related reinforcement learning and stochastic control areas.
AbstractList	Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dual dynamic programming method for solving single-scenario multi-stage optimization problems, by introducing novel mathematical tools including the saturation of search points. We then refine these basic tools and establish the iteration complexity for an explorative dual dynamic programing method proposed herein and the classic stochastic dual dynamic programming method for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption. Our results indicate that the complexity of these methods mildly increases with the number of stages T, in fact linearly dependent on T for discounted problems. Therefore, they are efficient for strategic decision making which involves a large number of stages, but with a relatively small number of decision variables in each stage. Without explicitly discretizing the state and action spaces, these methods might also be pertinent to the related reinforcement learning and stochastic control areas. Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dual dynamic programming method for solving single-scenario multi-stage optimization problems, by introducing novel mathematical tools including the saturation of search points. We then refine these basic tools and establish the iteration complexity for an explorative dual dynamic programing method proposed herein and the classic stochastic dual dynamic programming method for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption. Our results indicate that the complexity of these methods mildly increases with the number of stages T , in fact linearly dependent on T for discounted problems. Therefore, they are efficient for strategic decision making which involves a large number of stages, but with a relatively small number of decision variables in each stage. Without explicitly discretizing the state and action spaces, these methods might also be pertinent to the related reinforcement learning and stochastic control areas.
Audience	Academic
Author	Lan, Guanghui
Author_xml	– sequence: 1 givenname: Guanghui surname: Lan fullname: Lan, Guanghui email: george.lan@isye.gatech.edu organization: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
BookMark	eNp9kM9LwzAUx4NMcJv-A54GnjvfS9M0PY7hLxh40XNIk7RmtM1MOnD_vdEKggfJIeTx_eS991mQ2eAHS8g1whoBytuIgFBmQCEDLHiZ4RmZI8t5xjjjMzIHoEVWcIQLsohxDwCYCzEnuPX9obMfbjytfLOKo9dvKo5Or8xRdStzGlSfHofg26D63g3tJTlvVBft1c-9JK_3dy_bx2z3_PC03ewynRdizCxqTbWwRhlj6oLTSiAtS84qpsqmLmptKNMoNLNCc80bRoWidWMEWqVrkS_JzfRv6v1-tHGUe38MQ2opKc9RVIyJIqXWU6pVnZVuaPwYlE7H2DR3ktS4VN-UkFesKhgkQEyADj7GYBup3ahG54cEuk4iyC-jcjIqk1H5bVRiQukf9BBcr8LpfyifoJjCQ2vD7xr_UJ_A2Yp1
CitedBy_id	crossref_primary_10_1007_s00245_023_09977_1 crossref_primary_10_1137_22M1508005 crossref_primary_10_1287_opre_2020_0464 crossref_primary_10_1007_s12190_022_01722_1 crossref_primary_10_1137_23M1575093 crossref_primary_10_1007_s10107_024_02192_y crossref_primary_10_1007_s10107_022_01798_4 crossref_primary_10_1109_JSYST_2023_3305511
Cites_doi	10.1007/BF01582895 10.1287/opre.33.5.989 10.2139/ssrn.3102988 10.1016/j.ejor.2010.08.007 10.1287/opre.2018.1835 10.1287/moor.2014.0664 10.1287/moor.16.1.119 10.1016/j.orl.2005.02.003 10.1039/C9RE00176J 10.1007/s10107-018-1249-5 10.1007/s10107-011-0442-6 10.1016/S0927-0507(03)10003-5 10.1137/1.9780898718751 10.1287/moor.16.3.650 10.1287/opre.2013.1175 10.1007/s10107-014-0787-8 10.1007/978-3-030-39568-1 10.1007/s10957-004-1842-z 10.1007/s10589-013-9584-1 10.1137/19M1258876 10.1007/978-1-4419-8853-9
ContentType	Journal Article
Copyright	Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020 COPYRIGHT 2022 Springer Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020.
Copyright_xml	– notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020 – notice: COPYRIGHT 2022 Springer – notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020.
DBID	AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D
DOI	10.1007/s10107-020-01567-1
DatabaseName	CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional
DatabaseTitleList	Computer and Information Systems Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1436-4646
EndPage	754
ExternalDocumentID	A703949540 10_1007_s10107_020_01567_1
GroupedDBID	--K --Z -52 -5D -5G -BR -EM -Y2 -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 199 1B1 1N0 1OL 1SB 203 28- 29M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 6TJ 78A 7WY 88I 8AO 8FE 8FG 8FL 8TC 8UJ 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMOZ AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. B0M BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EAD EAP EBA EBLON EBR EBS EBU ECS EDO EIOEI EJD EMI EMK EPL ESBYG EST ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I-F I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAS LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQ- NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RIG RNI RNS ROL RPX RPZ RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 XPP YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8T Z8W Z92 ZL0 ZMTXR ZWQNP ~02 ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADXHL AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c358t-e1cc2c8edadddb5629812776494a7fb5bcd24c18c4e8c6c6f428a2bfd81eacb83
IEDL.DBID	RSV
ISICitedReferencesCount	16
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000569585000003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0025-5610
IngestDate	Thu Sep 25 00:40:13 EDT 2025 Sat Nov 29 10:25:33 EST 2025 Tue Nov 18 22:41:14 EST 2025 Sat Nov 29 03:34:02 EST 2025 Fri Feb 21 02:47:25 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	90C06 93A14 90C15 49M37 90C25 90C22
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c358t-e1cc2c8edadddb5629812776494a7fb5bcd24c18c4e8c6c6f428a2bfd81eacb83
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
PQID	2631894485
PQPubID	25307
PageCount	38
ParticipantIDs	proquest_journals_2631894485 gale_infotracacademiconefile_A703949540 crossref_citationtrail_10_1007_s10107_020_01567_1 crossref_primary_10_1007_s10107_020_01567_1 springer_journals_10_1007_s10107_020_01567_1
PublicationCentury	2000
PublicationDate	2022-02-01
PublicationDateYYYYMMDD	2022-02-01
PublicationDate_xml	– month: 02 year: 2022 text: 2022-02-01 day: 01
PublicationDecade	2020
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationSubtitle	A Publication of the Mathematical Optimization Society
PublicationTitle	Mathematical programming
PublicationTitleAbbrev	Math. Program
PublicationYear	2022
Publisher	Springer Berlin Heidelberg Springer Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer – name: Springer Nature B.V
References	Philpott, A., Wahid, F., Bonnans, F.: Midas: A mixed integer dynamic approximation scheme, 2016. PhD thesis, Inria Saclay Ile de France (2016) Tyrrell RockafellarRWetsRoger J-BScenarios and policy aggregation in optimization under uncertaintyMath. Oper. Res.1991161119147110679310.1287/moor.16.1.119 Baucke, R., Downward, A., Zakeri, G.: A deterministic algorithm for solving multistage stochastic programming problems. Technical report, The University of Auckland, 70 Symonds Street, Grafton, Auckland, July 2017 (2017) DonohueCJBirgeJRThe abridged nested decomposition method for multistage stochastic linear programs with relatively complete recourseAlgorithm. Oper. Res.2006112022763221148.90336 LinowskyKPhilpottABOn the convergence of sampling-based decomposition algorithms for multistage stochastic programsJ. Optim. Theory Appl.2005125349366213650010.1007/s10957-004-1842-z PhilpottAMatosVdFinardiEOn solving multistage stochastic programs with coherent risk measuresOper. Res.201361957970310573910.1287/opre.2013.1175 ShapiroAOn complexity of multistage stochastic programsOper. Res. Lett.20063418218606610.1016/j.orl.2005.02.003 BirgeJRLouveauxFVIntroduction to Stochastic Programming1997New YorkSpringer0892.90142 HindsbergerMPhilpottABResa: a method for solving multistage stochastic linear programsJ. Appl. Oper. Res.201461215 KelleyJEThe cutting plane method for solving convex programsJ. SIAM196087037121185380098.12104 LanGFirst-Order and Stochastic Optimization Methods for Machine Learning2020BaselSpringer10.1007/978-3-030-39568-1 LeclèreVCarpentierPChancelierJPLenoirAPacaudFExact converging bounds for stochastic dual dynamic programming via fenchel dualitySIAM J. Optim.202030212231250409188410.1137/19M1258876 Shapiro, A., Nemirovski, A.: On complexity of stochastic programming problems. E-print available at: http://www.optimization-online.org (2004) PereiraMPintoLMulti-stage stochastic optimization applied to energy planningMath. Program.1991521–3359375112617610.1007/BF01582895 GeorghiouATsoukalasAWiesemannWRobust dual dynamic programmingOper. Res.2019673813830396844110.1287/opre.2018.1835 GuiguesVSddp for some interstage dependent risk-averse problems and application to hydro-thermal planningComput. Optim. Appl.201457167203314650410.1007/s10589-013-9584-1 ZouJAhmedSSunXAStochastic dual dynamic integer programmingMath. Program.20191751–2461502394289710.1007/s10107-018-1249-5 BaoHZhouZKotsalisGLanGTongZLignin valorization process control under feedstock uncertainty through a dynamic stochastic programming approachReact. Chem. Eng.201941740174710.1039/C9RE00176J BirgeJRDecomposition and partitioning methods for multistage stochastic linear programsOper. Res.1985335989100780691610.1287/opre.33.5.989 Guigues, V.: Inexact cuts in deterministic and stochastic dual dynamic programming applied to linear optimization problems (2018) HigleJLSenSStochastic decomposition: an algorithm for two-stage linear programs with recourseMath. Oper. Res.199116650669112047510.1287/moor.16.3.650 Lan, G., Zhou, Z.: Dynamic stochastic approximation for multi-stage stochastic optimization. Manuscript, Georgia Institute of Technology, 2017. Mathematical Programming, under minor revision (2017) ShapiroAAnalysis of stochastic dual dynamic programming methodEur. J. Oper. Res.20112096372274685410.1016/j.ejor.2010.08.007 GirardeauPLeclereVPhilpottABOn the convergence of decomposition methods for multistage stochastic convex programsMath. Oper. Res.201540130145332041710.1287/moor.2014.0664 LanGNemirovskiASShapiroAValidation analysis of mirror descent stochastic approximation methodMath. Program.2012134425458296131410.1007/s10107-011-0442-6 Ahmed, S., Cabral, F.G., Costa, B.F.P.D.: Stochastic lipschitz dynamic programming (2019) KozmíkVMortonDPEvaluating policies in risk-averse multi-stage stochastic programmingMath. Program.20151521–2275300336948310.1007/s10107-014-0787-8 NesterovYEIntroductory Lectures on Convex Optimization: A Basic Course2004Norwell, MAKluwer Academic Publishers10.1007/978-1-4419-8853-9 RuszczyńskiARuszczyńskiAShapiroADecomposition methodsStochastic Programming2003AmsterdamElsevier14121110.1016/S0927-0507(03)10003-5 ShapiroADentchevaDRuszczyńskiALectures on Stochastic Programming: Modeling and Theory2009PhiladelphiaSIAM10.1137/1.9780898718751 V Kozmík (1567_CR14) 2015; 152 R Tyrrell Rockafellar (1567_CR24) 1991; 16 J Zou (1567_CR30) 2019; 175 A Shapiro (1567_CR28) 2009 G Lan (1567_CR15) 2020 A Philpott (1567_CR22) 2013; 61 JR Birge (1567_CR5) 1997 V Guigues (1567_CR9) 2014; 57 H Bao (1567_CR2) 2019; 4 1567_CR17 1567_CR1 1567_CR10 1567_CR3 JR Birge (1567_CR4) 1985; 33 JE Kelley (1567_CR13) 1960; 8 YE Nesterov (1567_CR20) 2004 M Pereira (1567_CR21) 1991; 52 CJ Donohue (1567_CR6) 2006; 1 A Georghiou (1567_CR7) 2019; 67 JL Higle (1567_CR11) 1991; 16 M Hindsberger (1567_CR12) 2014; 6 A Ruszczyński (1567_CR25) 2003 1567_CR29 A Shapiro (1567_CR27) 2011; 209 G Lan (1567_CR16) 2012; 134 A Shapiro (1567_CR26) 2006; 34 V Leclère (1567_CR18) 2020; 30 1567_CR23 K Linowsky (1567_CR19) 2005; 125 P Girardeau (1567_CR8) 2015; 40
References_xml	– reference: BaoHZhouZKotsalisGLanGTongZLignin valorization process control under feedstock uncertainty through a dynamic stochastic programming approachReact. Chem. Eng.201941740174710.1039/C9RE00176J – reference: PhilpottAMatosVdFinardiEOn solving multistage stochastic programs with coherent risk measuresOper. Res.201361957970310573910.1287/opre.2013.1175 – reference: HigleJLSenSStochastic decomposition: an algorithm for two-stage linear programs with recourseMath. Oper. Res.199116650669112047510.1287/moor.16.3.650 – reference: KelleyJEThe cutting plane method for solving convex programsJ. SIAM196087037121185380098.12104 – reference: GuiguesVSddp for some interstage dependent risk-averse problems and application to hydro-thermal planningComput. Optim. Appl.201457167203314650410.1007/s10589-013-9584-1 – reference: BirgeJRDecomposition and partitioning methods for multistage stochastic linear programsOper. Res.1985335989100780691610.1287/opre.33.5.989 – reference: KozmíkVMortonDPEvaluating policies in risk-averse multi-stage stochastic programmingMath. Program.20151521–2275300336948310.1007/s10107-014-0787-8 – reference: LanGNemirovskiASShapiroAValidation analysis of mirror descent stochastic approximation methodMath. Program.2012134425458296131410.1007/s10107-011-0442-6 – reference: Tyrrell RockafellarRWetsRoger J-BScenarios and policy aggregation in optimization under uncertaintyMath. Oper. Res.1991161119147110679310.1287/moor.16.1.119 – reference: HindsbergerMPhilpottABResa: a method for solving multistage stochastic linear programsJ. Appl. Oper. Res.201461215 – reference: GirardeauPLeclereVPhilpottABOn the convergence of decomposition methods for multistage stochastic convex programsMath. Oper. Res.201540130145332041710.1287/moor.2014.0664 – reference: LeclèreVCarpentierPChancelierJPLenoirAPacaudFExact converging bounds for stochastic dual dynamic programming via fenchel dualitySIAM J. Optim.202030212231250409188410.1137/19M1258876 – reference: ZouJAhmedSSunXAStochastic dual dynamic integer programmingMath. Program.20191751–2461502394289710.1007/s10107-018-1249-5 – reference: DonohueCJBirgeJRThe abridged nested decomposition method for multistage stochastic linear programs with relatively complete recourseAlgorithm. Oper. Res.2006112022763221148.90336 – reference: Philpott, A., Wahid, F., Bonnans, F.: Midas: A mixed integer dynamic approximation scheme, 2016. PhD thesis, Inria Saclay Ile de France (2016) – reference: PereiraMPintoLMulti-stage stochastic optimization applied to energy planningMath. Program.1991521–3359375112617610.1007/BF01582895 – reference: Shapiro, A., Nemirovski, A.: On complexity of stochastic programming problems. E-print available at: http://www.optimization-online.org (2004) – reference: Guigues, V.: Inexact cuts in deterministic and stochastic dual dynamic programming applied to linear optimization problems (2018) – reference: ShapiroADentchevaDRuszczyńskiALectures on Stochastic Programming: Modeling and Theory2009PhiladelphiaSIAM10.1137/1.9780898718751 – reference: ShapiroAAnalysis of stochastic dual dynamic programming methodEur. J. Oper. Res.20112096372274685410.1016/j.ejor.2010.08.007 – reference: BirgeJRLouveauxFVIntroduction to Stochastic Programming1997New YorkSpringer0892.90142 – reference: LanGFirst-Order and Stochastic Optimization Methods for Machine Learning2020BaselSpringer10.1007/978-3-030-39568-1 – reference: Ahmed, S., Cabral, F.G., Costa, B.F.P.D.: Stochastic lipschitz dynamic programming (2019) – reference: GeorghiouATsoukalasAWiesemannWRobust dual dynamic programmingOper. Res.2019673813830396844110.1287/opre.2018.1835 – reference: ShapiroAOn complexity of multistage stochastic programsOper. Res. Lett.20063418218606610.1016/j.orl.2005.02.003 – reference: LinowskyKPhilpottABOn the convergence of sampling-based decomposition algorithms for multistage stochastic programsJ. Optim. Theory Appl.2005125349366213650010.1007/s10957-004-1842-z – reference: Lan, G., Zhou, Z.: Dynamic stochastic approximation for multi-stage stochastic optimization. Manuscript, Georgia Institute of Technology, 2017. Mathematical Programming, under minor revision (2017) – reference: Baucke, R., Downward, A., Zakeri, G.: A deterministic algorithm for solving multistage stochastic programming problems. Technical report, The University of Auckland, 70 Symonds Street, Grafton, Auckland, July 2017 (2017) – reference: NesterovYEIntroductory Lectures on Convex Optimization: A Basic Course2004Norwell, MAKluwer Academic Publishers10.1007/978-1-4419-8853-9 – reference: RuszczyńskiARuszczyńskiAShapiroADecomposition methodsStochastic Programming2003AmsterdamElsevier14121110.1016/S0927-0507(03)10003-5 – volume: 52 start-page: 359 issue: 1–3 year: 1991 ident: 1567_CR21 publication-title: Math. Program. doi: 10.1007/BF01582895 – volume: 33 start-page: 989 issue: 5 year: 1985 ident: 1567_CR4 publication-title: Oper. Res. doi: 10.1287/opre.33.5.989 – ident: 1567_CR10 doi: 10.2139/ssrn.3102988 – ident: 1567_CR23 – volume-title: Introduction to Stochastic Programming year: 1997 ident: 1567_CR5 – ident: 1567_CR29 – ident: 1567_CR1 – ident: 1567_CR3 – volume: 209 start-page: 63 year: 2011 ident: 1567_CR27 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2010.08.007 – volume: 67 start-page: 813 issue: 3 year: 2019 ident: 1567_CR7 publication-title: Oper. Res. doi: 10.1287/opre.2018.1835 – volume: 6 start-page: 2 issue: 1 year: 2014 ident: 1567_CR12 publication-title: J. Appl. Oper. Res. – volume: 40 start-page: 130 year: 2015 ident: 1567_CR8 publication-title: Math. Oper. Res. doi: 10.1287/moor.2014.0664 – volume: 16 start-page: 119 issue: 1 year: 1991 ident: 1567_CR24 publication-title: Math. Oper. Res. doi: 10.1287/moor.16.1.119 – volume: 34 start-page: 1 year: 2006 ident: 1567_CR26 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2005.02.003 – volume: 4 start-page: 1740 year: 2019 ident: 1567_CR2 publication-title: React. Chem. Eng. doi: 10.1039/C9RE00176J – volume: 175 start-page: 461 issue: 1–2 year: 2019 ident: 1567_CR30 publication-title: Math. Program. doi: 10.1007/s10107-018-1249-5 – volume: 8 start-page: 703 year: 1960 ident: 1567_CR13 publication-title: J. SIAM – volume: 134 start-page: 425 year: 2012 ident: 1567_CR16 publication-title: Math. Program. doi: 10.1007/s10107-011-0442-6 – start-page: 141 volume-title: Stochastic Programming year: 2003 ident: 1567_CR25 doi: 10.1016/S0927-0507(03)10003-5 – volume-title: Lectures on Stochastic Programming: Modeling and Theory year: 2009 ident: 1567_CR28 doi: 10.1137/1.9780898718751 – volume: 16 start-page: 650 year: 1991 ident: 1567_CR11 publication-title: Math. Oper. Res. doi: 10.1287/moor.16.3.650 – volume: 61 start-page: 957 year: 2013 ident: 1567_CR22 publication-title: Oper. Res. doi: 10.1287/opre.2013.1175 – volume: 152 start-page: 275 issue: 1–2 year: 2015 ident: 1567_CR14 publication-title: Math. Program. doi: 10.1007/s10107-014-0787-8 – volume-title: First-Order and Stochastic Optimization Methods for Machine Learning year: 2020 ident: 1567_CR15 doi: 10.1007/978-3-030-39568-1 – volume: 125 start-page: 349 year: 2005 ident: 1567_CR19 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-004-1842-z – volume: 57 start-page: 167 year: 2014 ident: 1567_CR9 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-013-9584-1 – volume: 30 start-page: 1223 issue: 2 year: 2020 ident: 1567_CR18 publication-title: SIAM J. Optim. doi: 10.1137/19M1258876 – volume-title: Introductory Lectures on Convex Optimization: A Basic Course year: 2004 ident: 1567_CR20 doi: 10.1007/978-1-4419-8853-9 – volume: 1 start-page: 20 issue: 1 year: 2006 ident: 1567_CR6 publication-title: Algorithm. Oper. Res. – ident: 1567_CR17
SSID	ssj0001388
Score	2.4270473
Snippet	Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its...
SourceID	proquest gale crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	717
SubjectTerms	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Complexity Decision making Dynamic programming Flying-machines Full Length Paper Iterative methods Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimal control Optimization Stochastic processes Theoretical
Title	Complexity of stochastic dual dynamic programming
URI	https://link.springer.com/article/10.1007/s10107-020-01567-1 https://www.proquest.com/docview/2631894485
Volume	191
WOSCitedRecordID	wos000569585000003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1436-4646 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB5EPejBt7i6Sg-CBy30kTbJcREXLy7ii72FZpqioLuyrYL_3kk33V2foMfSdFpmkm8mzcw3AIeZyMltYOpjwLXPyAH72gjjG50HvJBSFynWzSZ4ryf6fXnpisLKJtu9OZKskXqm2C20v9Uim0iV0PKmPc8CuTthGzZcXd9N8DeMhWgatdrowJXKfC_jgzv6DMpfTkdrp9Nd_d_nrsGKCzK9znhWrMOcGWzA8gz1IF1dTPhay00ILSxYaszqzRsWHgWEeJ9ZBmfPlmp5-bhtveeSuZ5Iwhbcds9uTs9910zBxzgRlW9CxAiFyQnQck1RjyQbcZ4yyTJe6ERjHjEMBTIjMMW0oH1JFumCTEnYrEW8DfOD4cDsgBcnsdQ6ZTkJZoHhWcwzLlGQ549FEGMLwkanCh3TuG148aimHMlWOYqUo2rlqLAFx5Nnnsc8G7-OPrKmUnYRkmTMXC0BfZ-ls1IdwjFJWz8WtKDdWFO51VmqKCUkk7QxTVpw0lhvevvn9-7-bfgeLEW2WqJO8m7DfDV6MfuwiK_VQzk6qGftO3cI5Ek
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB5kFdSDb7G6ag-CBy30kTbJUcRFcV3EF3sLzTRFQXfFrYL_3km33fUNeixNp2Um-WbSzHwDsJOKjNwGJh76XHuMHLCnjTCe0ZnPcyl1nmDZbIJ3OqLbledVUdigznavjyRLpH5X7BbY32qhTaSKaXnTnmeSkceyjPkXlzcj_A0iIepGrTY6qEplvpfxwR19BuUvp6Ol02nN_-9zF2CuCjLdg-GsWIQJ01uC2XfUg3R1NuJrHSxDYGHBUmMWr24_dykgxNvUMji7tlTLzYZt690qmeuBJKzAdevo6vDYq5opeBjFovBMgBiiMBkBWqYp6pFkI84TJlnKcx1rzEKGgUBmBCaY5LQvSUOdkykJm7WIVqHR6_fMGrhRHEmtE5aRYOYbnkY85RIFef5I-BE6ENQ6VVgxjduGF_dqzJFslaNIOapUjgoc2Bs98zjk2fh19K41lbKLkCRjWtUS0PdZOit1QDgmaevHfAeatTVVtToHKkwIySRtTGMH9mvrjW___N71vw3fhunjq7O2ap90TjdgJrSVE2XCdxMaxdOz2YQpfCnuBk9b5Qx-AzLe5y0
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED9kiuiD3-J0ah8EH7SsH2mTPA51KOoQ_MC30FxTFHTKVgX_ey9du81PEB9L02u4S-4jufsdwE4iUjIbGLvoce0yMsCuNsK4Rqcez6TUWYxFswne6YjbW3kxVsVfZLtXV5KDmgaL0tTNm89p1hwrfPPtEVtgk6oi2uoU_0wym0hv4_XLm6Eu9kMhqqat1lMoy2a-p_HBNH1W0F9uSgsD1J7__9QXYK50Pp3WYLUswoTpLsHsGCQhPZ0PcVz7y-BbdWEhM_M35ylzyFHEu8QiOzu2hMtJB-3snTLJ65EorMB1--jq4Ngtmyy4GEYid42PGKAwKSm6VJM3JEl2nMdMsoRnOtKYBgx9gcwIjDHOKF5JAp2RiElnaxGuQq371DVr4IRRKLWOWUqEmWd4EvKESxTkEYTCC7EOfsVfhSUCuW2E8aBG2MmWOYqYowrmKL8Oe8Nvngf4G7-O3rViU3ZzEmVMyhoDmp-FuVIt0m-SQkLm1aFRSVaVu7avgpg0nKSANarDfiXJ0euf_7v-t-HbMH1x2FZnJ53TDZgJbEFFkQfegFreezGbMIWv-X2_t1Us5neQr_AR
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Complexity+of+stochastic+dual+dynamic+programming&rft.jtitle=Mathematical+programming&rft.au=Lan%2C+Guanghui&rft.date=2022-02-01&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=191&rft.issue=2&rft.spage=717&rft.epage=754&rft_id=info:doi/10.1007%2Fs10107-020-01567-1&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10107_020_01567_1
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-5610&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-5610&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-5610&client=summon