Polar Cones and Cone Capping in Hilbert Spaces

Paolo d’Alessandro

Chapter Chapter 11 in On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions, 2025, pp 183-195 from Springer

Abstract: Abstract Polarization is for cones what orthogonal complementation is for linear subspaces. Here we develop in detail the theory of polarization of cones, initiated within lcs, not only recasting in Hilbert space style most of the material developed therein but also adding some further major results, like the decomposition of the space in the direct sum of a closed cone plus its polar cone, which parallels the decomposition in the direct sum of a closed subspace and its orthogonal complement.

Date: 2025
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DOI: 10.1007/978-3-031-92477-4_11

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