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G-Polytopes and Generalization of Cone Capping

In: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions

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  • Paolo d’Alessandro

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.

Suggested Citation

  • Paolo d’Alessandro, 2025. "G-Polytopes and Generalization of Cone Capping," Springer Books, in: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions, chapter 0, pages 257-275, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92477-4_17
    DOI: 10.1007/978-3-031-92477-4_17
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