Article ID: | iaor20119968 |
Volume: | 151 |
Issue: | 1 |
Start Page Number: | 135 |
End Page Number: | 162 |
Publication Date: | Oct 2011 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Fliege Jrg, Xu Huifu |
Keywords: | programming: multiple criteria, stochastic processes |
We investigate one stage stochastic multiobjective optimization problems where the objectives are the expected values of random functions. Assuming that the closed form of the expected values is difficult to obtain, we apply the well known Sample Average Approximation (SAA) method to solve it. We propose a smoothing infinity norm scalarization approach to solve the SAA problem and analyse the convergence of efficient solution of the SAA problem to the original problem as sample sizes increase. Under some moderate conditions, we show that, with probability approaching one exponentially fast with the increase of sample size, an