The aim of this project consists in applying nonlinear probabilistic constraints to optimization problems in gas transportation assuming that the underlying random parameter obeys a multivariate and continuous distribution. Doing so, a robust in the sense of probability design of gas transport shall be facilitated. Stochastic optimization is the appropriate mathematical discipline to cope with uncertainty when looking for optimal decisions under random perturbations of some nominal parameters. Among different modeling options, probabilistic constraints hold a key position first of all in engineering applications. The solution of optimization problems with nonlinear probabilistic constraints with continuous multivariate distributions can be considered as new ground both from the theoretical and – at least for interesting dimension - from the numerical perspectives. Moreover, in the present project, we deal with implicit probabilistic constraints where the relation between decision and random parameter is established only by additional variables via some equation system. Although gas network problems with uncertain injection and consumption provide a very natural motivation for the research in this project, the mathematical insight to be expected has an impact on quite different applications as well, for instance, on optimization problems of power management, particularly those related with renewable energies. Beyond this, optimal control problems governed by PDEs and subjected to random state constraints promise being a potential application of implicit probabilistic constraints. In its first phase the project will investigate optimization problems arising from a simple stationary gas network model (RNET-ISO4) subject to random loads. Here the probabilistic constraint ensures the technical feasibility of loads with a specified probability. In the longer perspective, the consideration of dynamic probabilistic constraints for time-dependent decisions and of binary variables shall be pursued.
A poster to B04 can be found here.