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arXiv · 2201.05498

Convergence of an Asynchronous Block-Coordinate Forward-Backward Algorithm for Convex Composite Optimization

Cheik Traoré·Saverio Salzo·Silvia Villa
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Abstract

In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly according to an arbitrary probability distribution. We prove that the iterates generated by the algorithm form a stochastic quasi-Fej\'er sequence and thus converge almost surely to a minimizer of the objective function. Moreover, we prove a general sublinear rate of convergence in expectation for the function values and a linear rate of convergence in expectation under an error bound condition of Tseng type.

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Cheik Traoré, Saverio Salzo, Silvia Villa. 2022-01-14. Convergence of an Asynchronous Block-Coordinate Forward-Backward Algorithm for Convex Composite Optimization. https://arxiv.org/abs/2201.05498

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