The Strong Convergence of Proximal Alternating Direction Method of Multipliers in Real Hilbert Spaces
Abstract
The aim of this paper is to demonstrate that strong convergence corresponds well to the approximate alternating directions method (PADMM) in real infinite dimensional Hilbert spaces for convex optimization problems. Assuming that the solutions set for these problems are not empty, we demonstrate that the sequence generated by the PADMM is strongly convergent towards the optimal solution of the problem constrained convex optimization problems.
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