A Class Of Algorithms For Solving The Weighted Minimum Enclosing Ball Problem

In this thesis,the weighted minimum enclosing ball problem is studied in high dimensional space,which is widely used in data mining,facility location,computational geometry,artificial intelligence,collision detection,pattern recognition and so on.In fact,this problem is a non-smooth convex problem.Firstly,according to the idea of smooth approximation,CHKS smooth function and logexponential smooth function are used to approximate the objective function,and the weighted minimum enclosing ball problem is transformed into smooth unconstrained optimization problems.On this basis,two smooth approximation algorithms are proposed for solving this problem and their convergence analysis is given.Secondly,combined with smooth approximation algorithms and the special structure for the equivalent form of the weighted minimum enclosing ball problem,the inexact Newton conjugate gradient algorithm is proposed and its convergence analysis is given.Finally,data examples and numerical experiments are given to analyze the effectiveness of the algorithm proposed in this thesis.