Parallel processors for planning under uncertainty
Annals of Operations Research
Multi-stage stochastic optimization applied to energy planning
Mathematical Programming: Series A and B
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
On the convergence of algorithms with implications for stochastic and nondifferentiable optimization
Mathematics of Operations Research
Finite master programs in regularized stochastic decomposition
Mathematical Programming: Series A and B
New variants of bundle methods
Mathematical Programming: Series A and B
Computational complexity of stochastic programming problems
Mathematical Programming: Series A and B
The Scenario Generation Algorithm for Multistage Stochastic Linear Programming
Mathematics of Operations Research
Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics)
On complexity of multistage stochastic programs
Operations Research Letters
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In this paper we present a new approach to solving multi-stage stochastic decision models in the presence of constraints. The models themselves are stochastic linear programs (SLP), but we presume that their deterministic equivalent problems are too large to be solved exactly. We seek an asymptotically optimum solution by simulating the stochastic decomposition (SD) algorithmic process, originally designed for two-stage SLPs. When SD is implemented in a time-staged manner the algorithm begins to take the flavor of a simulation leading to what we refer to as optimization simulation. Among its major advantages, it can work directly with sample paths, and this feature makes the new algorithm much easier to integrate within a simulation. We also overcome certain limitations such as a stage-wise independence assumption required by other sampling-based algorithms for multi-stage stochastic programming. Finally, we also discuss how these methods can be interpreted as close relatives of approximate dynamic programming.