l1，l2，l∞范数下带约束的最小化最近距离和问题

Solving constrained closest minisum location problems under l_1,l_2,l_∞-norms

研究设备定位领域内的最小化距离和问题.与以往研究不同的是,文章用需求区域代替距离和问题中的需求点.问题的目标是在平面上的某约束区域内定位一个新的设备,使得新设备到各个需求区域的最近点的加权距离和达到最小,其中距离用lp范数来度量,称之为带约束的最小化最近距离和问题.此问题首先被转化为等价的变分不等式问题,此等价的转化使得投影收缩方法可用于求解相应的变分不等式.算法得到的序列收敛到问题的最优点.最后给出数值实验,实验结果证明算法是有效的.

This paper investigated a constrained minisum location problem with the demand points replaced by demand regions. The objective was to locate a new facility in a constrained area such that the sum of weighted distances from the facility to the closest points of demand regions was minimized. The distances were measured by lp -norms. This problem was transformed into an equivalent linear variational inequality. This transformation allowed that the problems under three popular distance measuring functions （ l1,l2,l∞ - norms） could be solved. It was assured that the iterates acquired by our suggested algorithm would converge to the optimal solution of the problem. Preliminary computational results were reported, which showed that the suggested algorithm was promising.