Solving k-center problems involving sets based on optimization techniques
Solving k-center problems involving sets based on optimization techniques
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DOI：
10.1007/s10898-019-00834-6
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发表时间：
2020-01
影响因子：
1.8
通讯作者：
N. T. An;N. M. Nam;X. Qin
中科院分区：
文献类型：
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作者：
N. T. An;N. M. Nam;X. Qin
连续中心问题的目的是寻找具有最小半径的k个球，以覆盖有限个给定的点。本文提出并研究了k-中心问题的如下推广形式：给定有限个非空闭凸集，寻找半径最小的k个球，使得它们的并集与所有的非空闭凸集相交.由于它的非光滑性和非凸性，这个问题是非常具有挑战性的。基于非光滑优化技术，我们首先推导出问题的一些定性性质，然后提出新的算法来解决这个问题。数值实验表明了算法的有效性。
The continuousk-center problem aims at findingkballs with the smallest radius to cover a finite number of given points in. In this paper, we propose and study the following generalized version of thek-center problem: Given a finite number of nonempty closed convex sets in, findkballs with the smallest radius such that their union intersects all of the sets. Because of its nonsmoothness and nonconvexity, this problem is very challenging. Based on nonsmooth optimization techniques, we first derive some qualitative properties of the problem and then propose new algorithms to solve the problem. Numerical experiments are also provided to show the effectiveness of the proposed algorithms.