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• W3101080484 abstract "Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper we establish numerous properties of amenable cones and investigate the relationships between amenability and other properties of convex cones, such as niceness and projectional exposure. We show that the amenability of a compact slice of a closed convex cone is equivalent to the amenability of the cone, and we prove several results on the preservation of amenability under intersections and other convex operations. It then follows that homogeneous, doubly nonnegative, and other cones that can be represented as slices of the cone of positive semidefinite matrices are amenable. It is known that projectionally exposed cones are amenable and that amenable cones are nice; however, the converse statements have been open questions. We construct an example of a four-dimensional cone that is nice but not amenable. We also show that amenable cones are projectionally exposed in dimensions up to and including four. We conclude with a discussion on open problems related to facial structure of convex sets that we came across in the course of this work but were not able to fully resolve." @default.
• W3101080484 created "2020-11-23" @default.
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• W3101080484 date "2022-09-01" @default.
• W3101080484 modified "2023-10-15" @default.
• W3101080484 title "Amenable Cones Are Particularly Nice" @default.
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• W3101080484 doi "https://doi.org/10.1137/20m138466x" @default.
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