球约束点的加权成对距离和的一个界
A Bound on the Sum of Weighted Pairwise Distances of Points Constrained to Balls
摘要：
我们考虑的问题，选择欧几里德点，以最大限度地提高他们的加权成对距离的总和，当每个点被约束到一个球中心在原点。我们推导出一个对偶最小化问题，并显示出强对偶性（即，所得的上界是紧的）。我们勾勒出一个多项式时间算法找到一个接近最优的点集。
英文摘要：
We consider the problem of choosing Euclidean points to maximize the sum of their weighted pairwise distances, when each point is constrained to a ball centered at the origin. We derive a dual minimization problem and show strong duality holds (i.e., the resulting upper bound is tight) when some locally optimal configuration of points is affinely independent. We sketch a polynomial time algorithm for finding a near-optimal set of points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
