(SPEPS)
Institute for Operations Research and the Management Sciences (Linthicum, Md.)
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| edoc-Server der Humboldt-Universität zu Berlin |
| 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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Endnote Bibtex |
| 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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