Stochastic Dynamic Linear Programming: A Sequential Sampling Algorithm for Multistage Stochastic Linear Programming

Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear programming (MSLP) problems often rely upon scenario trees to represent the underlying stochastic process. When this process exhibits stagewise independence, sampling-based techniques, particularly the … Read more

An Adaptive Sequential Sample Average Approximation Framework for Solving Two-stage Stochastic Programs

We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations as follows: during each outer iteration, a sample-path problem is implicitly generated using a sample of observations or “scenarios,” and solved only \emph{imprecisely}, to within a … Read more

Stochastic Decomposition for Two-stage Stochastic Linear Programs with Random Cost Coefficients

Stochastic decomposition (SD) has been a computationally effective approach to solve large-scale stochastic programming (SP) problems arising in practical applications. By using incremental sampling, this approach is designed to discover an appropriate sample size for a given SP instance, thus precluding the need for either scenario reduction or arbitrary sample sizes to create sample average … Read more