Explain the difference between Alternating Direction Method of Multipliers(ADMM) and coordinate descent (CD) .

The alrernating direction method of multipliers(ADMM) is an algorithm that solves convex optimization problems by breaking them into smoller pieces, each of which are them easier to handle. ot has recently found wide application in a number of areas but, coordinate descent is an optimization algotithm that successively minimizes along coordinate direction to find the minimum of a dunction. At each iteration, the algorithm determined a coordinate or coordinate blockvia a coordinate selection rule, then exectly or inerctly minimizes over the corresponding coordinates or coordinate block. Coordinate descent is applicable in both differentiable and devivative-free contexts.