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A note on the alternating direction method of multipliers. (English) Zbl 1255.90093
Summary: We consider the linearly constrained separable convex programming, whose objective function is separable into $$m$$ individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case $$m=2$$, while it remains open whether its convergence can be extended to the general case $$m\geq 3$$. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.

MSC:
 90C25 Convex programming
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References:
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