增广拉格朗日函数的两种分解方法比较

Comparison of Two Decomposition Approaches with the Augmented Lagrangian Function

分解方法是一种把复杂的大规模优化问题分解成各个子问题来求解的方法。增广拉格朗日松弛方法的一个主要缺点是它的二次项是不可分离的。可将辅助问题原理方法或分块坐标下降方法应用于增广拉格朗日松弛,来处理增广拉格朗日函数的不可分离性。通过线性约束Ax+By=z的优化问题对这两种分解方法进行比较。

The decomposition methods are used to solve large-scale optimization problem by decomposition them into sub-problems.The main drawback of the augmented Lagrangian relaxation metheod is that the quadratic term introduced by the augmented Lagrangian is not separable.To cope with the non-separability of the augmented Lagrangian function,we can apply auxiliary problem principle(APP)method or block coordinate descent(BCD) method.In this paper we compare these two decomposition methods solving optimization problem with linear constraints.