摘要
考虑在n维空间中求m个球的最小闭包球(the Smallest Enclosing Ball,SEB)问题.首先将SEB问题转化为一个含有函数max(0,z)的等价无约束非光滑凸优化问题,然后利用光滑化技巧和有限内存BFGS方法来求解高维空间中的SEB问题,并分析了方法的收敛性.数值实验结果表明文中给出的算法是有效的.
Consider the problem of computing the smallest enclosing ball of a set composed of m balls in n dimension space.First,the problem is transformed into an unconstrained convex optimization problem involving the maximum function max（0,z）,then the smoothing technique and the limited memory BFGS method are used to solve SEB problem in high dimensions,and also the convergence of the algorithm is proved.Numerical results indicate the effectiveness of the algorithm.
出处
《系统科学与数学》
CSCD
北大核心
2013年第5期617-625,共9页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61179040
61072144)资助课题
