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arXiv · 1604.04845

A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization

Meng Wen·Yu-Chao Tang·Jigen Peng
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Abstract

We consider an inertial primal-dual algorithm to compute the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a stochastic coordinate descent inertial primal-dual splitting algorithm. Moreover, in order to prove the convergence of the proposed inertial algorithm, we formulate first the inertial version of the randomized Krasnosel'skii-Mann iterations algorithm for approximating the set of fixed points of a nonexpansive operator and investigate its convergence properties. Then the convergence of stochastic coordinate descent inertial primal-dual splitting algorithm is derived by applying the inertial version of the randomized Krasnosel'skii-Mann iterations to the composition of the proximity operator.

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Meng Wen, Yu-Chao Tang, Jigen Peng. 2016-04-17. A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization. https://arxiv.org/abs/1604.04845

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