Random block coordinate methods for inconsistent convex optimisation problems

2022/12/22 by Staudigl, Mathias, Jacquot, Paulin · 1 citation
#90B10 #90C06 #90C25 #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Optimization and Control (math.OC) #and Science (cs.CE)

paper · doi:10.48550/arxiv.2212.12045

Abstract

We develop a novel randomised block coordinate 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/k²) complexity rates in the convex and strongly convex case, respectively, k being the iteration count. Motivated by the increased complexity in the control of distribution level electric 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 \reviseas dual variables in our optimisation framework.

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