2014/08/19 by Vincent Guigues, Guigues, Vincent · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #90C15 #90C90 #Economic and Environmental Valuation #FOS: Mathematics #Health Systems, Economic Evaluations, Quality of Life #Optimization and Control (math.OC) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1408.4439
openalex publication_date 2014/08/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider a class of sampling-based decomposition methods to solve\nrisk-averse multistage stochastic convex programs. We prove a formula for the\ncomputation of the cuts necessary to build the outer linearizations of the\nrecourse functions. This formula can be used to obtain an efficient\nimplementation of Stochastic Dual Dynamic Programming applied to convex\nnonlinear problems. We prove the almost sure convergence of these decomposition\nmethods when the relatively complete recourse assumption holds. We also prove\nthe almost sure convergence of these algorithms when applied to risk-averse\nmultistage stochastic linear programs that do not satisfy the relatively\ncomplete recourse assumption. The analysis is first done assuming the\nunderlying stochastic process is interstage independent and discrete, with a\nfinite set of possible realizations at each stage. We then indicate two ways of\nextending the methods and convergence analysis to the case when the process is\ninterstage dependent.\n