This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Pennanen, T. Search for Related Content

Epi-Convergent Discretizations of Multistage Stochastic Programs

Department of Management Science, Helsinki School of Economics, PL 1210, 00101 Helsinki, Finland
pennanen{at}hkkk.fi

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.

Key Words: multistage stochastic program; discretization; epi-convergence
History: Received: October 12, 2003; revision received: April 29, 2004;