摘要
陈中文研究中关于求线性方程组极小l1范数解问题有着较为广泛的应用.本文研究了该问题的最优性条件,给出最优解的充分必要条件.进一步研究了该问题最优解的一种表现形式,提出一个单纯形方法的算法,该算法解决了退化问题,且收敛速度较快,同时给出确定初始基的方法.
The problem of solving the minimum l 1 norm solution of an underdetermined system of linear equations is extensively used in many fields. In this paper, we first study the optimal condition, and present a necessary and sufficient condition for the optimal solution of problem. We also give an expression of the optimal solution of problem. Based on these theorems, an algorithm for solving problem, that is a simplex method, is built. The algorithm can solve the problem of the degenerate case, and the convergence rate is fast.
出处
《淮阴师范学院学报（自然科学版）》
CAS
2003年第1期13-18,57,共7页
Journal of Huaiyin Teachers College;Natural Science Edition
关键词
极小l1范数解
最优性条件
算法
minimum l1 norm solution
optimal condition
algorithm
