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

Abstract

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.