加权最小包容球问题的对偶光滑逼近算法  

A Dual Smooth Approximation Algorithm for Solving the Weighted Minimum Enclosing Ball Problem

作　　者：胡平 蒋毅 HU Ping;JIANG Yi(Key Laboratory of Visual Computing and Virtual Reality of Sichuan Province,School of Mathematical Science,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院可视化计算与虚拟现实四川省重点实验室,成都610068

出　　处：《重庆师范大学学报（自然科学版）》2022年第5期7-13,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11201324);教育部霍英东基金(No.141114);四川省自然科学青年基金(No.2022NSFSC1852)。

摘　　要：【目的】研究加权最小包容球问题,并给出一类求解该问题的算法。【方法】加权最小包容球问题是一个极大极小化的非光滑问题。首先利用对偶方法将该问题转化为极小化非光滑问题,然后利用光滑逼近思想,将该问题转化为极小化的光滑问题进行求解。【结果】根据数据实例表明该算法有效。【结论】得到求解加权最小包容球问题的一类对偶光滑逼近算法。[Purposes]To study the weighted minimum enclosing ball problem and give a class of algorithm for solving the problem. [Methods]The problem of the weighted minimum enclosing ball is a maxmin non-smooth problem. Firstly, the dual method is used to transform the problem into a minimization non-smooth problem. Secondly, the problem is transformed into minimization smoothing problems by the idea of smooth approximation. [Findings]The data examples show that the algorithm is effective. [Conclusions]A class of dual smooth approximation algorithm for solving the weighted minimum enclosing ball problem is obtained.

关 键 词：加权最小包容球 极大极小问题 非光滑优化 光滑逼近 有限内存L-BFGS方法 

分 类 号：O221.1[理学—运筹学与控制论]