Epi-convergent discretizations of multistage stochastic programs via integration quadratures

TY - JOUR

T1 - Epi-convergent discretizations of multistage stochastic programs via integration quadratures

AU - Pennanen, Teemu

PY - 2009/1

Y1 - 2009/1

N2 - 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.

AB - 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.

U2 - 10.1007/s10107-007-0113-9

DO - 10.1007/s10107-007-0113-9

M3 - Article

SN - 0025-5610

VL - 116

SP - 461

EP - 479

JO - MATHEMATICAL PROGRAMMING

JF - MATHEMATICAL PROGRAMMING

IS - 1-2

ER -