Concept

Schönhardt polyhedron

Publications associées (6)

Structural Screening and Design of Platinum Nanosamples for Oxygen Reduction

Nanocatalyst-by-design promises to empower the next generation of electrodes for energy devices. However, current numerical methods consider individual and often geometrical closed-shell nanoparticles, neglecting how the coexistence of several and structur ...

AMER CHEMICAL SOC2020

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018

On Sub-determinants and the Diameter of Polyhedra

Friedrich Eisenbrand, Martin Niemeier, Nicolai Hähnle, Marco Di Summa, Nicolas Bonifas

We derive a new upper bound on the diameter of a polyhedron , where . The bound is polynomial in and the largest absolute value of a sub-determinant of , denoted by . More precisely, we show that the diameter of is bounded by . If is bounded, then we show ...

Springer2014

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

Particle Manifold Method (PMM) for Multiscale Continuous-Discontinuous Analysis

Liang Sun

It is important to consider the microstructure of a material when studying the macroscopic mechanical properties. Although special equipments have been used for micromechanics study through experimental tests, it is limited by instruments and reproducibili ...

EPFL2012

On canonical representation of convex polyhedra

Stefano Picozzi

Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...

EPFL2005