增广拉格朗日函数的两种可分化方法之比较  

Comparison of Two Decomposition Approaches with the Augmented Lagrangian Function

作　　者：王磊[1] 白富生[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2010年第6期7-11,26,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10171118)

摘　　要：可分方法用于将一个复杂的大规模优化问题分解成各个子问题进行求解。增广拉格朗日松弛方法的主要缺点是由其引入的二次项是不能分离的。为了处理这种增广拉格朗日函数的不可分离性,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方法。与已有文献中对带有约束条件x-x-=0的优化问题进行这两种可分方法的比较不同,本文对带有更一般的约束条件——线性约束z=Ax的优化问题进行这两种可分化方法的比较;最后给出的两个算例证实了本文的理论分析结果——在处理不可分离的增广拉格朗日函数的时候,在一定条件下,分块坐标下降法往往比辅助问题原则法更快得到最优值。The decomposition methods are used to solve large-scale optimization problems by decomposition them into sub-problems.The main drawback of the augmented Lagrangian relaxation method 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 to the augmented Lagrangian relaxation method.Compared with the literature in solving the optimization problem with constraints x-x=0,we compare these two decomposition methods solving optimization problem with more general constraints——linear constrains z=Ax.Two numerical examples are to show comparison of theoretical validation—In dealing with non-separable augmented Lagrangian function,we can often expect faster performance of the BCD method compared to the APP method under certain conditions.

关 键 词：可分化方法 增广拉格朗日松弛 辅助问题原理 分块坐标下降 

分 类 号：O221.2[理学—运筹学与控制论]