Scenario cluster Lagrangean decomposition for risk averse in multistage stochastic optimization

2017 ◽  
Vol 85 ◽  
pp. 154-171 ◽  
Author(s):  
Laureano F. Escudero ◽  
María Araceli Garín ◽  
Aitziber Unzueta
Keyword(s):  
Stochastic Optimization ◽  
Risk Averse ◽  
Lagrangean Decomposition ◽  
Multistage Stochastic Optimization ◽  
Scenario Cluster

Cluster Lagrangean decomposition in multistage stochastic optimization

2016 ◽  
Vol 67 ◽  
pp. 48-62 ◽  
Author(s):  
Laureano F. Escudero ◽  
María Araceli Garín ◽  
Aitziber Unzueta
Keyword(s):  
Stochastic Optimization ◽  
Lagrangean Decomposition ◽  
Multistage Stochastic Optimization

A Model of Multistage Risk-Averse Stochastic Optimization and its Solution by Scenario-Based Decomposition Algorithms

2020 ◽  
Vol 37 (04) ◽  
pp. 2040004
Author(s):  
Min Zhang ◽  
Liangshao Hou ◽  
Jie Sun ◽  
Ailing Yan
Keyword(s):  
Stochastic Optimization ◽  
Financial Management ◽  
Mean Deviation ◽  
Decomposition Algorithms ◽  
Risk Averse ◽  
Stochastic Variational Inequalities ◽  
Business Operations ◽  
Convergence Results ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm

Stochastic optimization models based on risk-averse measures are of essential importance in financial management and business operations. This paper studies new algorithms for a popular class of these models, namely, the mean-deviation models in multistage decision making under uncertainty. It is argued that these types of problems enjoy a scenario-decomposable structure, which could be utilized in an efficient progressive hedging procedure. In case that linkage constraints arise in reformulations of the original problem, a Lagrange progressive hedging algorithm could be utilized to solve the reformulated problem. Convergence results of the algorithms are obtained based on the recent development of the Lagrangian form of stochastic variational inequalities. Numerical results are provided to show the effectiveness of the proposed algorithms.

scholarly journals Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems

2020 ◽  
Vol 186 (3) ◽  
pp. 985-1005
Author(s):  
Pierre Carpentier ◽  
Jean-Philippe Chancelier ◽  
Michel De Lara ◽  
François Pacaud
Keyword(s):  
Stochastic Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Multistage Stochastic Optimization
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