Spherical Convex Hull Membership: Complexity and Performance of Geometric and Accelerated Methods

We study the problem of testing membership of the origin in the convex hull of $n$ unit vectors in $\mathbb{R}^m$, seeking a convex combination of norm at most $\varepsilon$ or a strict separating hyperplane. The Spherical Triangle Algorithm (STA) uses nearest-point updates on pivot segments. We fir