Convex geometry of quantum resource quantification

Convex Geometry of Orbits

We study metric properties of convex bodies B and their polars B, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Salesman Polytope in polyhedral combinatorics (G = Sn, the symmetric group), the set of nonnegative polynomials in real algebraic geometry (G = SO(n), the special orthogonal group), and the convex hull of the Grassmannian ...

Convex Optimal Uncertainty Quantification

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient ...

Convex and Discrete Geometry

Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...

Math 341: Convex Geometry

Max-Plus Convex Geometry

Max-plus analogues of linear spaces, convex sets, and polyhedra have appeared in several works. We survey their main geometrical properties, including max-plus versions of the separation theorem, existence of linear and non-linear projectors, max-plus analogues of the Minkowski-Weyl theorem, and the characterization of the analogues of “simplicial” cones in terms of distributive lattices.