There are two basic angles associated with a pair of linear subspaces: the Diximier angle and Friedrichs angle. These classical notions, which date back to first half 20th century, have been thoroughly studied due their utility in description convergence rates for various projection-based algorithms solving feasibility problems. The Dixmier orthogonal complements is same as original provided ...

We study the class of (locally) anti-blocking bodies as well some associated classes convex bodies. For these bodies, we prove geometric inequalities regarding volumes and mixed volumes, including Godbersen’s conjecture, near-optimal bounds on Mahler Saint-Raymond-type reverse Kleitman for volumes. apply our results to combinatorics posets Sidorenko-type linear extensions pairs [Formula: see te...

We give explicit polynomial-sized (in n and k) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree k in n variables. These convex cones form a family of non-polyhedral outer approximations of the non-negative orthant that preserve low-dimensional faces while successively discarding high-dimensional faces. More generally we const...