Distributed proximal augmented Lagrangian method for nonsmooth composite optimization
Sepideh Hassan-Moghaddam, Mihailo R. Jovanović · 2018
We study a class of nonsmooth composite optimization problems in which the convex objective function is given by a sum of differentiable and nondifferentiable terms. By introducing auxiliary variables in nondifferentiable terms, we provide an equivalent consensus-based characterization that is convenient for distributed implementation. The Moreau envelope associated with the nonsmooth part of the objective function is used to bring the optimization problem into a continuously differentiable form that serves as a basis for the development of a primal-descent dual-ascent gradient flow method. This algorithm exploits separability of the objective function and is well-suited for in-network optimization. We prove global asymptotic stability of the proposed algorithm and solve the problem of growing undirected consensus networks in a distributed manner to demonstrate its effectiveness.