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In this paper we consider a novel partitioned framework for distributedoptimization in peer-to-peer networks. In several important applications theagents of a network have to solve an optimization problem with two keyfeatures: (i) the dimension of the decision variable depends on the networksize, and (ii) cost function and constraints have a sparsity structure relatedto the communication graph. For this class of problems a straightforwardapplication of existing consensus methods would show two inefficiencies: poorscalability and redundancy of shared information. We propose an asynchronousdistributed algorithm, based on dual decomposition and coordinate methods, tosolve partitioned optimization problems. We show that, by exploiting theproblem structure, the solution can be partitioned among the nodes, so thateach node just stores a local copy of a portion of the decision variable(rather than a copy of the entire decision vector) and solves a small-scalelocal problem.

Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition