求解加权最小包容球问题的两种算法  

Two Algorithms for Solving Weighted Minimum Enclosing Ball Problem

作　　者：胡平 蒋毅 周子意 李金菊 HU Ping;JIANG Yi;ZHOU Ziyi;LI Jinju(School of Mathemaical Sciences,Sichuan Normal Uniceniy,Chenghu 60066 Sichuan;V.C.&V.R.Key Lab,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2023年第3期326-335,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11201324);教育部霍英东基金(141114);四川省科技计划(2022ZYD0011和2022NSFSC1852)。

摘　　要：研究在高维空间中的加权最小包容球问题,该问题是非光滑的凸优化问题.提出光滑逼近和非精确牛顿共轭梯度算法求解该问题,并证明其收敛性.此外,给出数值实验,比较这2种算法和经典牛顿共轭梯度算法的计算效率,其中非精确牛顿共轭梯度算法的计算效率更高.In this paper,we study the weighted minimum enclosing ball problem in high-dimensional space,which is a non-smooth convex optimization problem.Smooth approximation and inexact Newton conjugate gradient algorithms for solving the problem are proposed,and the convergence are proved.The numerical experiments are given to compare the computational efficiency of the two algorithms proposed in this paper and the classical Newton conjugate gradient algorithm.The results show that inexact Newton conjugate gradient algorithm is more efficient than others.

关 键 词：加权最小包容球问题 光滑逼近 非精确牛顿共轭梯度算法 

分 类 号：O221.2[理学—运筹学与控制论]