极小化r个最大函数和的二阶光滑化方法

Second-order Smoothing Method for Minimizing Sum of r-Largest Functions

已给m个定义在n维欧几里徳空间的函数,在这m个函数中求r个最大值函数和的最小值,其中1≤r≤m。这个问题在定位分析领域有重要的应用。显然该问题是非光滑最优化问题,不能直接用牛顿法或拟牛顿法来求解。该问题转化为只包含最大值函数max{0,t}的非光滑问题,对该非光滑问题提出一种具有全局收敛的二阶光滑化算法。

Given a collection of m functions defined on Rn,the sum of the r largest functions of the collection is minimized,where 1≤r≤m.The problem of the minimizing the sum of the r largest functions has important applications in the area of location analysis.It is obvious that this problem is nonsmooth optimization problem.It can not be solved by using Newton or qusi-Newton unconstrained minimization algorithms.This paper reformulates the problem as a nonsmooth problem that only involves the maximum function max and develops a new globally convergent second-order smoothing method.