For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's endpoints and eccentricity $\sqrt 3 / 2$. Using an optimization approach, we prove that the convex sets bounded by these ellipses intersect, answering a Tverberg-type question of Andy Fingerhut from 1995.

翻译：对于平面上偶数个点构成的集合，选取一个最大和匹配（即最大化边欧氏距离之和的完美匹配）。针对最大和匹配中的每条边，考虑以其端点为焦点、离心率为$\sqrt 3 / 2$的椭圆。通过优化方法，我们证明这些椭圆所围成的凸集存在交叠，从而回答了Andy Fingerhut于1995年提出的一个Tverberg型问题。