Einstein-Hessian barriers on convex cones

Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications

In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...

1 0 Ju n 20 16 REMARKS ON CURVATURE IN THE TRANSPORTATION METRIC

According to a classical result of E. Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the “hyperbolic” toric Kähler-Einstein equation e = detDΦ on proper convex cones. We prove a generalization of this theorem showing that for every Φ solving this equation...

Some Results on Boundedness in Locally Convex Cones

Primal-Dual Interior-Point Methods for Self-Scaled Cones

In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex quadratically constrained quadratic prog...

O ct 2 01 7 EXTREMAL KÄHLER - EINSTEIN METRIC FOR TWO - DIMENSIONAL CONVEX BODIES

Given a convex body K ⊂ Rn with the barycenter at the origin we consider the corresponding Kähler-Einstein equation e = detDΦ. If K is a simplex, then the Ricci tensor of the Hessian metric DΦ is constant and equals n−1 4(n+1) . We conjecture that the Ricci tensor of D Φ for arbitrary K is uniformly bounded by n−1 4(n+1) and verify this conjecture in the two-dimensional case. The general case r...