Probabilistic constrained optimization on flow networks

Abstract Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and model with uncertain boundary data on networks. We introduce two different ways how to compute the probability for random be feasible, discussing their advantages disadvantages. context, feasible means, that corresponding meets some box constraints at network junctions. The first method is spheric radial decomposition second kernel density estimation. both settings, certain optimization problems derivatives of probabilistic constraint using estimator. Moreover, derive necessary optimality conditions approximated problem case. Throughout use numerical examples illustrate our results by comparing them classical Monte Carlo approach desired probability.