TY - ELEC
AU - James Saunderson
PY - 2019
TI - Limitations on the expressive power of convex cones without long chains of faces
LA - eng
M3 - Moving Image
AB - Recently Averkov showed that various convex cones related to nonnegative polynomials do not have K-lifts (representations as projections of linear sections of K) where K is a Cartesian product of positive semidefinite cones of "small" size. In this talk I'll discuss an extension of this result that says that convex bodies with certain neighborliness properties do not have K-lifts whenever K is a Cartesian product of cones, each of which does not have any long chains of faces (such as smooth cones, low-dimensional cones, and cones defined by hyperbolic polynomials of low degree).
N2 - Recently Averkov showed that various convex cones related to nonnegative polynomials do not have K-lifts (representations as projections of linear sections of K) where K is a Cartesian product of positive semidefinite cones of "small" size. In this talk I'll discuss an extension of this result that says that convex bodies with certain neighborliness properties do not have K-lifts whenever K is a Cartesian product of cones, each of which does not have any long chains of faces (such as smooth cones, low-dimensional cones, and cones defined by hyperbolic polynomials of low degree).
UR - https://open.library.ubc.ca/collections/48630/items/1.0385848
ER - End of Reference