Multi-Agent asynchronous nonconvex large-scale optimization

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. The proposed algorithmic framework is distributed and asynchronous: i) agents update their variables at arbitrary times, without any coordination with the others; and ii) agents may use outdated information from their neighbors. Convergence to stationary solutions is proved, and theoretical complexity results are provided, showing nearly ideal linear speedup with respect to the number of agents, when the delays are not too large.