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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 $m\ge 3$. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.
MSC:
 90C25 Convex programming
References:
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