2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109832Let $K$ be a full-dimensional convex subset of $\mathbb{R}^n$. We describe a new polynomial-time Turing reduction from the weak separation problem for $K$ to the weak optimization problem for $K$ that is based on a geometric heuristic. We compare our reduction, which relies on analytic centers, with the standard, more general reduction.Data Structures and AlgorithmsOptimization and Controltext