关于为一组点定中心的问题

ON THE PROBLEMS OF LOCATING A CENTER FOR A GROUP OF POINTS

作者考虑如下的为一组点定中心的问题：设Ｘ１，…，Ｘｍ是平面上（或Ｒｎ中）的一组点，需要求得一个点Ｘ，使得诸Ｘ；与Ｘ的距离的偏差最小．依据对偏差的不同的度量方法，问题可归结为不同的最优化问题．本文分析了三个这样的问题，它们分别可表示为线性ｍｉｎｍａｘ问题和ｄ．Ｃ．规划问题．文中还讨论了可能的求解这些问题的数值方法．

e consider the following problems of locating a center for a group of points.Let x1,…,xm be points in a phne(or Rn).It is required to find a point x.which minimizes the errors between x and every xi.In this paper,we study three such problems which use different criteria to measure the errors.Some numerical methods for these problems is also investigated.