|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|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Keywords (eng):||epi-convergence, multistage stochastic program, discretization|
Mathematics of operations research 1 (Vol. 30, 2005)
Institute for Operations Research and the Management Sciences (Linthicum, Md.)
|Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link.||Endnote Bibtex|
|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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