Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty

2016 ◽  
Vol 28 (3) ◽  
pp. 385-404 ◽  
Author(s):  
Weini Zhang ◽  
Hamed Rahimian ◽  
Güzin Bayraksan
Keyword(s):  
Water Allocation ◽  
Decomposition Algorithms ◽  
Risk Averse ◽  
Stochastic Programs ◽  
Multistage Stochastic Programs

Structure of risk-averse multistage stochastic programs

OR Spectrum ◽  
2014 ◽  
Vol 37 (3) ◽  
pp. 559-582 ◽  
Author(s):  
Jitka Dupačová ◽  
Václav Kozmík
Keyword(s):  
Risk Averse ◽  
Stochastic Programs ◽  
Multistage Stochastic Programs

Consistency of Sample Estimates of Risk Averse Stochastic Programs

2013 ◽  
Vol 50 (02) ◽  
pp. 533-541 ◽  
Author(s):  
Alexander Shapiro
Keyword(s):  
Stochastic Programming ◽  
Law Of Large Numbers ◽  
Risk Measures ◽  
Regularity Conditions ◽  
Distributed Data ◽  
Risk Averse ◽  
Asymptotic Consistency ◽  
Stochastic Programs ◽  
Large Numbers ◽  
Independent Identically Distributed

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

A Scalable Bounding Method for Multistage Stochastic Programs

2017 ◽  
Vol 27 (3) ◽  
pp. 1772-1800 ◽  
Author(s):  
Burhaneddi̇n Sandikçi ◽  
Osman Y. Özaltin
Keyword(s):  
Stochastic Programs ◽  
Multistage Stochastic Programs

Periodical Multistage Stochastic Programs

2020 ◽  
Vol 30 (3) ◽  
pp. 2083-2102
Author(s):  
Alexander Shapiro ◽  
Lingquan Ding
Keyword(s):  
Stochastic Programs ◽  
Multistage Stochastic Programs

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.

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