Amenable Cones Are Particularly Nice

Amenability is a geometric property of convex cones that stronger than facial exposedness and assists in the study error bounds for conic feasibility problems. In this paper we establish numerous properties amenable investigate relationships between amenability other cones, such as niceness projectional exposure. We show compact slice closed cone equivalent to cone, prove several results on preservation under intersections operations. It then follows homogeneous, doubly nonnegative, can be represented slices positive semidefinite matrices are amenable. known projectionally exposed nice; however, converse statements have been open questions. construct an example four-dimensional nice but not also dimensions up including four. conclude with discussion problems related structure sets came across course work were able fully resolve.