Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang, Projecting onto rectangular hyperbolic paraboloids in Hilbert space

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DOI: 10.23952/asvao.5.2023.2.04
Volume 5, Issue 2, 1 August 2023, Pages 163-180

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.

How to Cite this Article:
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang, Projecting onto rectangular hyperbolic paraboloids in Hilbert space, Appl. Set-Valued Anal. Optim. 5 (2023), 163-180.