G-Polytopes and Generalization of Cone Capping

Paolo d’Alessandro

Chapter Chapter 17 in On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions, 2025, pp 257-275 from Springer

Abstract: Abstract We introduce the notion of g-polytope and that of g-capping of a closed convex cone, which, respectively, generalize the notions of weakly compact set and that of a cappable cone. Then we develop both a theory of g-polytopes, which are closed convex sets containing no rays, and a corresponding theory of generalized capping of convex cones, where we require that the cut cone be a g-polytope, instead of a convex weakly compact set. We will also prove a KM-like theorem for the special class of g-polytopes, which occur in the range space theory of polyhedra.

Date: 2025
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DOI: 10.1007/978-3-031-92477-4_17

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