In this note, we extend the existing algorithms Extra and subgradient-push to a new algorithm called ExtraPush for convex consensus optimization over a directed network. When the network is stationary, we propose a simplified algorithm called Normalized ExtraPush. These algorithms use a fixed step size like in Extra and accept the column-stochastic mixing matrices like in subgradient-push. We present preliminary analysis for ExtraPush under a bounded sequence assumption. For Normalized ExtraPush, we show that it naturally produces a bounded, linearly convergent sequence provided that the objective function is strongly convex.
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