4 research outputs found
Minimal pairs of polytopes and their number of vertices
We define what is called Blaschke difference for polytopes as an inverse operation to Blaschke addition. Using this operation we give a new algorithm to reduce and find a minimal pair of polytopes from the given class of the Rådström-Hörmander lattice containing a pair of polytopes in IR2. This method gives a better algorithmic insight and easy to handle than the one given by Handschug (1989). We also prove that a pair of polytopes in the plane is minimal if and only if the sum of the number of their vertices is minimal in the class. However, it is shown in the paper that, this last statement does not hold true in general for higher dimensional spaces
Nondifferentiable Optimization: Motivations and Applications
IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984.
This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications