Epi-convergent discretizations of multistage stochastic programs via integration quadratures

Authors:
Teemu Pennanen
Affiliations:
Helsinki School of Economics, Department of Business Technology, PL 1210, 00101, Helsinki, Finland
Venue:
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Year:
2008

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Abstract

This paper presents procedures for constructing numerically solvable discretizations of multistage stochastic programs that epi-converge to the original problem as the discretizations are made finer. Epi-convergence implies, in particular, that the cluster points of the first-stage solutions of the discretized problems are optimal first-stage solutions of the original problem. The discretization procedures apply to a general class of nonlinear stochastic programs where the uncertain factors are driven by time series models. Using existing routines for numerical integration allows for an easy and efficient implementation of the procedures.