Distributed Random Block-Coordinate descent methods for ill-posed composite convex optimisation problems
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We develop a novel randomised block coordinate descent primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying in the midway between the celebrated Chambolle-Pock primal-dual algorithm and Tseng's accelerated proximal gradient method, we establish global convergence of the last iterate as well optimal O(1/k) and O(1/k^2) complexity rates in the convex and strongly convex case, respectively, k being the iteration count. Motivated by distributed and data-driven control of power systems, we test the performance of our method on a second-order cone relaxation of an AC-OPF problem. Distributed control is achieved via the distributed locational marginal prices (DLMPs), which are obtained dual variables in our optimisation framework.
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