求解绝对值方程稀疏解的增广拉格朗日方法

Augmented Lagrangian method for solving sparse solutions of absolute value equations

设计了一类求绝对值方程稀疏解的增广拉格朗日方法.首先将绝对值方程稀疏解问题转换成含不等式约束的线性规划问题.然后将该线性规划视为4块可分离的凸规划问题,进而设计了求解该凸规划问题增广拉格朗日方法.与经典的增广拉格朗日方法不同,该方法包含了一个带常数步长的校正步,同时与其他类似方法相比,该步长的取值范围更大.利用该方法求解绝对值方程的稀疏解.数值结果验证了方法的可行性与有效性.

In this paper,a kind of augmented Lagrangian method for solving the sparse solution of absolute value equations is designed.Firstly,the problem of the sparse solution of absolute value equations is transformed into a linear programming problem with inequality constraints.Then the linear programming is regarded as a four-block separable convex programming problem,and a augmented Lagrangian method is designed to solve the convex programming problem.Different from the classical augmented Lagrangian method,this method includes a correction step with constant step size,and compared with other similar methods,the range of this step size is larger.The sparse solution of the absolute value equation is solved by this method.The numerical results verify the feasibility and effectiveness of the method.