We propose a novel algorithmic framework for the asynchronous and distributed optimization of multi-agent systems. We consider the constrained minimization of a nonconvex and nonsmooth partially separable sum-utility function, i.e., the cost function of each agent depends on the optimization variables of that agent and of its neighbors. This partitioned setting arises in several applications of practical interest.
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than current state-of-the-art models.
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