Orbitopes

By Raman Sanyal, Frank Sottile, Bernd Sturmfels. 2009

77 citations recorded by the source corpus.

An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector space. These highly symmetric convex bodies lie at the crossroads of several fields, in particular convex geometry, optimization, and algebraic geometry. We present a self-contained theory of orbitopes, with particular emphasis on instances arising from the groups SO(n) and O(n). These include Schur-Horn orbitopes, tautological orbitopes, Caratheodory orbitopes, Veronese orbitopes and Grassmann orbitopes. We study their face lattices, their algebraic boundary hypersurfaces, and representations as spectrahedra or projected spectrahedra.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c55a2e1f2d126c9365b8db5d1a9a14b841501f45

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

Citations in the corpus

Compressed Sensing Off the Grid (2012, background): “…this curve is characterizable in terms of linear matrix inequalities, and membership in the convex hull can thus be computed in polynomial time (see [25] for a proof of this result and a discussion of many other algebraic varieties whose convex hulls are characterized by semide ﬁ nite programming).”