Linear and quadratic programming in oriented matroids

Multiparametric Linear and Quadratic Programming

In this work we present an algorithm for the solution of multiparametric linear and quadratic programming problems.With linear constraints and linear or convex quadratic objective functions, the optimal solution of these optimization problems is given by a conditional piecewise linear function of the varying parameters. This function results from first-order estimations of the analytical nonlin...

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Separoids and characterization of linear uniform oriented matroids

In this paper the geometric dimension of an oriented matroid is introduced. It is the minimal euclidian dimension where its separoid (to be defined) can be realized as a family of convex sets. We show that in the uniform case, it is enough to know this invariant to decide if the oriented matroid is linear .

Oriented Matroids

The theory of oriented matroids provides a broad setting in which to model, describe, and analyze combinatorial properties of geometric configurations. Apparently totally different mathematical objects such as point and vector configurations, arrangements of hyperplanes, convex polytopes, directed graphs, and linear programs find a common generalization in the language of oriented matroids. The...

Flows in Oriented Matroids

Recently Hochstättler and Nešetřil [3] introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. We describe the structure and the dimension of the flow lattice for uniform and rank 3 oriented matroids and co...