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Horoballs and the subgradient method
March 26, 2024, 4:43 a.m. | Adrian S. Lewis, Genaro Lopez-Acedo, Adriana Nicolae
cs.LG updates on arXiv.org arxiv.org
Abstract: To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically convex: the methods are described using tangent spaces and exponential maps. By contrast, our iteration applies in a general Hadamard space, is framed in the underlying space itself, and relies instead on horospherical convexity of the objective level sets. For this …
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