Multilinear approximation on rectangles and the related moment problem

The Edmundson-Madansky (E-M) inequality provides an upper bound of the expectation of a convex function of a random vector, provided the components of the random vector are stochastically independent. Frauendorfer and Kall extended the E-M inequality to the dependent case. This paper provides the natural algebraic setting for this extension. It is shown that multilinear approximation is the basic idea. The results and the calculations are simplified considerably by the use of Kronecker products. Moreover, the class of all functions for which the general E-M bound holds is characterized completely. It includes many nonconvex functions, for instance the multi-chord-dominated functions, which include the multiconvex functions

INVESTMENT EVALUATION BASED ON THE COMMERCIAL SCOPE - THE PRODUCTION OF NATURAL-GAS

The annual production planning of a natural gas trading and transporting company is modelled as a linear system of (in)equalities. The model is used to quantify the increase of robustness with respect to commercial uncertainty, resulting from investments in production capacities. A novel concept is the commercial scope, describing the set of future commercial scenarios that can be handled effectively. It is shown how relevant parts of the boundary of this set can be constructed using induced constraints. A numerical example is presented