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

Vincent Guigues (vincent.guigues***at***gmail.com)

Abstract: 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.

Keywords: Stochastic programming; Risk-averse optimization; Decomposition algorithms; Monte Carlo sampling; Relatively complete recourse; SDDP

Category 1: Stochastic Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 08/19/2014
Entry Accepted: 08/20/2014
Entry Last Modified: 09/09/2016

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