Polar Degrees
摘要
The notion of polar degrees is fundamental for assessing the algebraic complexity of polynomial optimization problems of a metric origin.We already recognized this point for Euclidean distance optimization in Section 2.3, and we will see it again in Theorem 5.5 for polyhedral norms, with focus on theWasserstein metric from optimal transport theory. The punchline is that polar degrees govern linear programming over real algebraic varieties.