On augmented Lagrangian decomposition methods for multistage stochastic programs

Charles H. Rosa; Andrzej Ruszczyński

doi:10.1007/BF02187650

On augmented Lagrangian decomposition methods for multistage stochastic programs

Charles H. Rosa
, Andrzej Ruszczyński

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.

Original language	American English
Pages (from-to)	289-309
Number of pages	21
Journal	Annals of Operations Research
Volume	64
DOIs	https://doi.org/10.1007/BF02187650
State	Published - 1996
Externally published	Yes

ASJC Scopus subject areas

General Decision Sciences
Management Science and Operations Research

Keywords

Augmented Lagrangian
Decomposition
Jacobi method
Parallel computation
Stochastic programming

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10.1007/BF02187650

Cite this

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title = "On augmented Lagrangian decomposition methods for multistage stochastic programs",

abstract = "A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.",

keywords = "Augmented Lagrangian, Decomposition, Jacobi method, Parallel computation, Stochastic programming",

author = "Rosa, \{Charles H.\} and Andrzej Ruszczy{\'n}ski",

year = "1996",

doi = "10.1007/BF02187650",

language = "American English",

volume = "64",

pages = "289--309",

journal = "Annals of Operations Research",

issn = "0254-5330",

publisher = "Springer Netherlands",

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TY - JOUR

T1 - On augmented Lagrangian decomposition methods for multistage stochastic programs

AU - Rosa, Charles H.

AU - Ruszczyński, Andrzej

PY - 1996

Y1 - 1996

N2 - A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.

AB - A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.

KW - Augmented Lagrangian

KW - Decomposition

KW - Jacobi method

KW - Parallel computation

KW - Stochastic programming

UR - https://www.scopus.com/pages/publications/21344437897

UR - https://www.scopus.com/pages/publications/21344437897#tab=citedBy

U2 - 10.1007/BF02187650

DO - 10.1007/BF02187650

M3 - Article

SN - 0254-5330

VL - 64

SP - 289

EP - 309

JO - Annals of Operations Research

JF - Annals of Operations Research

ER -

On augmented Lagrangian decomposition methods for multistage stochastic programs

Abstract

ASJC Scopus subject areas

Keywords

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