Robust weighted expected residual minimization formulation for stochastic vector variational inequalities

In order to deal with (stochastic) multi-objective optimization problems, a robust Pareto optimal solution by minimizing the worst case weighted sum of objectives on a given weight set is considered [J. Hu, S. Mehrotra, Oper. Res., 60 (2011), 936–953], [J. Hu, T. Homem-de-Mello, S. Mehrotra, Manuscript, (2010)]. Based on this idea, we introduce a new class of deterministic model for stochastic vector variational inequalities, called robust weighted expected residual minimization model. Then we propose sample average approximation (SAA) approach to solve robust weighted expected residual minimization problems. Some convergence results are established for the approximation problem in terms of the optimal value and the set of optimal solutions.