Epi-convergent discretizations of multistage stochastic programs

Epi-convergent discretizations of multistage stochastic programs

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Article ID: iaor20061421
Country: United States
Volume: 30
Issue: 1
Start Page Number: 245
End Page Number: 256
Publication Date: Feb 2005
Journal: Mathematics of Operations Research
Authors:
Abstract:

In many dynamic stochastic optimization problems in practice, the uncertain factors are best modeled as random variables with an infinite support. The 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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