How to solve optimization problem using Alternating Direction Minimization (ADM) algorithm with Lagrangian multiplier in Matlab?

2020 9 30
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I have the following optimization problem that is solved using Alternative Direction Minimization (ADM) algorithm with Lagrangian multiptier however I don't know how to implement this in Matlab. Is there a Function for ADM in Matlab? or Does anyone know how to implement this in Matlab? Any help will be appreciated with many thanks.

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