基于ADM分解的预测-校正分解算法

The Predictor Correcting Decomposition Method of Basing on the Alternating Direction

考虑的是一种具有线性约束条件且目标函数是块可分的凸优化极小问题,文章的目标函数主要是由三个凸函数之和组成.解决这种模型,理论上有效的处理办法是直接拓展的交替方向乘子法,简称EADM法,该方法是在交替方向乘子法(ADMM法)的基础上演变而来.但是这种方法的收敛性目前在理论上还没有得到证明.因此,基于ADM法的直接拓展以及在韩德仁文章的指引下,本文刻画了一种新的分离方法,称为基于ADM分解的预测-校正分解算法,该方法也能解决这种模型.新方法在每次迭代的时候,通过一个轻微的校正计算产生一个新的迭代,从而校正了直接拓展的ADM法的输出结果.本文证明了新方法在适当假设条件下的全局收敛性,并通过有关例子说明了该方法具有可行性.

We consider the convexity minimum problem with a linear constraints and a block separable objective function.The objective function is composed of sum of three convex functions.Theoretically,an effective solution to the model is directly expanding alternating direction method of multiplies,for short EADM,which is based on the alternating direction method(ADMM).But its convergence property abstractly does not establish.Therefore,with guidance of directly expanding alternating direction method of multiplies and Han′s paper,this article proposes a new method-the predictor correcting decomposition method based on the alternating direction,which can also solve this model.When it iterates,the new method can generate another iteration by slight correcting.Thus,it corrects the consequence of directly expanding alternating direction method of multiplies.The article proves that the new method has a global convergence property in proper given conditions and explains that new method has feasible property with associative examples.