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: | Pennanen Teemu |
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.