The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear\nequality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM\nmethod. In this paper, we will show that no matter how small the step size and the penalty parameter are, the convergence of the\nparallel splitting ALM is not guaranteed. We propose a new convergent parallel splitting ALM (PSALM), which is the regularizing\nALMâ??s minimization subproblem by some simple proximal terms. In application this new PSALM is used to solve video\nbackground extraction problems and our numerical results indicate that this new PSALM is efficient.
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