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arXiv · 2206.04878

Projecting onto rectangular hyperbolic paraboloids in Hilbert space

Heinz H. Bauschke·Manish Krishan Lal·Xianfu Wang
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Abstract

In $\mathbb{R}^3$, a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic paraboloids in $\mathbb{R}^n$. Motivated by his work, we provide a rigorous analysis of the associated projection. In some cases, finding this projection amounts to finding a certain root of a quintic or cubic polynomial. We also observe when the projection is not a singleton and point out connections to graphical and set convergence.

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Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang. 2022-06-10. Projecting onto rectangular hyperbolic paraboloids in Hilbert space. https://doi.org/10.23952/asvao.5.2023.2.04

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