三个可分离算子凸优化的线性化方法

A LINEARIZED METHOD FOR THE SEPARABLE CONVEX PROGRAMMING WITH OBJECTIVE FUNCTION REPRESENTED AS THREE FUNCTIONS

本文研究了三个可分离算子不含交叉变量的线性约束凸优化问题.利用定制的邻近点算法,对其变分不等式子问题进行线性化处理,并增加一邻近点项,使其子问题成为易于运算的单调线性变分不等式,得到了线性化定制的邻近点算法,并证明了全局收敛性,推广了文献中的研究结果.

In this paper, we study the convex minimization problem with linear constraints and a block-separable objective function which is represented as the sum of three functions without coupled variables. Based on the customized proximal point algorithm, linearing its variable inequality subproblem and adding an approximate item to the subproblem, the new linearized method is offered and its global convergence is proved finally. The results have extended the corresponding studies documented.