Centerpoints: A Link between Optimization and Convex Geometry
本文提出一个统一多种“中心点”概念的新定义，基于此开发了用于凸混合整数优化的oracle算法，并证明这类算法在某种意义下是最优的，同时给出了计算这些点的有效方法。
We introduce a concept that generalizes several different notions of a “centerpoint” in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are “best possible” in a certain sense. Motivated by this, we establish structural results about this concept and provide efficient algorithms for computing these points. Our main motivation is to understand the complexity of oracle-based convex mixed-integer optimization.