Predictive Modeling in a Polyhedral Optimization Space

Polyhedral techniques in combinatorial optimization

Generally, combinatorial optimization problems are easy to formulate, but hard to solve. The most successfull approaches, cutting plane algorithms and column generation, rely on the (mixed) integer linear programming formulation of a problem. The theory of polyhedra, i.e., polyhedral combinatorics, is the foundation of these techniques. This manuscript intends to give an overview of polyhedral ...

Optimization of polyhedral terrains

Polyhedral Methods in Discrete Optimization

In the last decade our capability of solving integer programming problems has increased dramatically due to the effectiveness of cutting plane methods based on polyhedral investigations. Polyhedral cutting planes have become central features in optimization software packages for integer programming. Here we present some of the important polyhedral methods used in discrete optimization. We discu...

Polyhedral Covers of Tree Space

The phylogenetic tree space, introduced by Billera, Holmes, and Vogtmann, is a cone over a simplicial complex. In this short article, we construct this complex from local gluings of classical polytopes, the associahedron and the permutohedron. Its homotopy is also reinterpreted and calculated based on polytope data.

A Projective Framework for Polyhedral Mesh Modeling

We present a novel framework for polyhedral mesh editing with face-based projective maps, that preserves planarity by definition. Such meshes are essential in the field of architectural design and rationalization. By using homogeneous coordinates to describe vertices, we can parametrize the entire shape space of planar-preserving deformations with bilinear equations. The generality of this spac...