Search results for "Convex polytope"

Convex bodies and convexity on Grassmann cones

1962

The Linear Ordering Polytope

2010

So far we developed a general integer programming approach for solving the LOP. It was based on the canonical IP formulation with equations and 3-dicycle inequalities which was then strengthened by generating mod-k-inequalities as cutting planes. In this chapter we will add further ingredients by looking for problem- specific inequalities. To this end we will study the convex hull of feasible solutions of the LOP: the so-called linear ordering polytope.

On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit

2010

We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.

Approximate convex hull of affine iterated function system attractors

2012

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

Characterizing extreme points of polyhedra an extension of a result by Wolfgang Bühler

1982

This paper reconsiders the characterization given by Buhler admitting convex polyhedra of probability distributions on a finite or countable set which are given by systems of linear inequalities more complex than those considered before.

Real quadrics in C n , complex manifolds and convex polytopes

2006

In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…

Predictive control of convex polyhedron LPV systems with Markov jumping parameters

2012

The problem of receding horizon predictive control of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of linear parameter varying system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficients matrices for the time variable system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic convex polyhedron linear parameter varying systems, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon…