A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
Concise formulas for the area and volume of a hyperspherical cap
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.