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On the convergence properties of a majorized alternating direction method of multipliers for linearly constrained convex optimization problems with coupled objective functions. (English) Zbl 1342.90130
Summary: In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers for linearly constrained convex optimization problems, whose objectives contain coupled functions. Our convergence analysis relies on the generalized Mean-Value Theorem, which plays an important role to properly control the cross terms due to the presence of coupled objective functions. Our results, in particular, show that directly applying two-block alternating direction method of multipliers with a large step length of the golden ratio to the linearly constrained convex optimization problem with a quadratically coupled objective function is convergent under mild conditions. We also provide several iteration complexity results for the algorithm.

##### MSC:
 90C25 Convex programming 68Q25 Analysis of algorithms and problem complexity 65K05 Numerical mathematical programming methods
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##### References:
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