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New primal-dual proximal algorithms for distributed optimization

Book Contribution - Book Chapter Conference Contribution

© 2016 IEEE. We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and can only communicate with its neighbors. The goal is to minimize the aggregate of the private cost functions and reach a consensus over a graph. We propose a primal-dual algorithm based on Asymmetric Forward-Backward-Adjoint (AFBA), a new operator splitting technique introduced recently by two of the authors. Our algorithm includes the method of Chambolle and Pock as a special case and has linear convergence rate when the cost functions are piecewise linear-quadratic. We show that our distributed algorithm is easy to implement without the need to perform matrix inversions or inner loops. We demonstrate through computational experiments how selecting the parameter of our algorithm can lead to larger step sizes and yield better performance.
Book: Proc. of 2016 IEEE 55th Conference on Decision and Control
Pages: 1959 - 1964
Publication year:2016