Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

Resumo

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Ficha do documento

Tipo

Artigo científico

Ano

2016

Instituição

EMAp - Escola de Matemática Aplicada

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Não informado

Identificador

oai:repositorio.fgv.br:10438/16239

Temas

Economia

Palavras-chave

Stochastic programmingRisk-averse optimizationDecomposition algorithmsMonte Carlo samplingRelatively complete recourseEconomiaProcesso estocásticoMonte Carlo, Método de