We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization (ERM) solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample averag...

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast amount of literature on the subject has appeared. The researchers in the field have never ceased to emphasize the inherent difficulties in solving stochastic programming problems, without ever giving a theoretical justification of thi...

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic ...

Placement of sensors in water distribution networks helps timely detection of contamination and reduces risk to the population. Identifying the optimal locations of these sensors is important from an economic perspective and has been previously attempted using the theory of optimization. This work extends that formulation by considering uncertainty in the network and describes a stochastic prog...