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Convex cones machinery is the mainstay of our investigations on geometry of convex sets and optimization. Here we present, within the Hilbert space environment, a major result on decomposition of non-closed convex cones, which have a closed lineality space (while the general case will be solved later on) and develop various important ancillary results.

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Convex Cones in Hilbert Spaces and Decomposition of Cones

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  • 发表日期：

    2025年

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  • Paolo d’Alessandro

摘要

Convex cones machinery is the mainstay of our investigations on geometry of convex sets and optimization. Here we present, within the Hilbert space environment, a major result on decomposition of non-closed convex cones, which have a closed lineality space (while the general case will be solved later on) and develop various important ancillary results.