Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems

A unified convergence theory is derived for a class of stationary iterative methods for solving linear equality constrained quadratic programs or saddle point problems.This class is constructed from essentially all possible splittings of the submatrix residing in the(1,1)-block of the augmented saddle point matrix that would produce non-expansive iterations.The classic augmented Lagrangian method and alternating direction method of multipliers are two special members of this class.