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SPEPS Preprint

Author(s): Teemu Pennanen, Helsinki School of Economics
Title: Epi-convergent discretizations of multistage stochastic programs
Date of Acceptance: 10.02.2004
Submission Date: 28.11.2003
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): epi-convergence, multistage stochastic program, discretization
Appeared in: Mathematics of operations research 1 (Vol. 30, 2005)
Institute for Operations Research and the Management Sciences (Linthicum, Md.)
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Abstract (eng):
In many dynamic stochastic optimization problems in practice, the uncertain factors are best modeled as random variables with an infinite support. This results in infinite-dimensional optimization problems that can rarely be solved directly. Therefore, the random variables (stochastic processes) are often approximated by finitely supported ones (scenario trees), which result in finite-dimensional optimization problems that are more likely to be solvable by available optimization tools. This paper presents conditions under which such finite-dimensional optimization problems can be shown to epi-converge to the original infinite-dimensional problem. Epi-convergence implies the convergence of optimal values and solutions as the discretizations are made finer. Our convergence result applies to a general class of convex problems where neither linearity nor complete recourse are assumed.
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