  Alternating direction method of multiplier (ADMM) is a powerful method to
solve decentralized convex optimization problems. In distributed settings, each
node performs computation with its local data and the local results are
exchanged among neighboring nodes in an iterative fashion. During this
iterative process the leakage of data privacy arises and can accumulate
significantly over many iterations, making it difficult to balance the
privacy-utility tradeoff. In this study we propose Recycled ADMM (R-ADMM),
where a linear approximation is applied to every even iteration, its solution
directly calculated using only results from the previous, odd iteration. It
turns out that under such a scheme, half of the updates incur no privacy loss
and require much less computation compared to the conventional ADMM. We obtain
a sufficient condition for the convergence of R-ADMM and provide the privacy
analysis based on objective perturbation.
