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Motivated by recent development in networking and parallel data-processing,we consider a distributed and localized finite-sum (or fixed-sum) allocationtechnique to solve resource-constrained convex optimization problems overmulti-agent networks (MANs). Such networks include (smart) agents representingan intelligent entity capable of communication, processing, anddecision-making. In particular, we consider problems subject to practicalnonlinear constraints on the dynamics of the agents in terms of theircommunications and actuation capabilities (referred to as the node dynamics),e.g., networks of mobile robots subject to actuator saturation and quantizedcommunication. The considered distributed sum-preserving optimization solutionfurther enables adding purposeful nonlinear constraints, for example,sign-based nonlinearities, to reach convergence in predefined-time or robust toimpulsive noise and disturbances in faulty environments. Moreover, convergencecan be achieved under minimal network connectivity requirements among theagents; thus, the solution is applicable over dynamic networks where thechannels come and go due to the agent's mobility and limited range. This paperdiscusses how various nonlinearity constraints on the optimization problem(e.g., collaborative allocation of resources) can be addressed for differentapplications via a distributed setup (over a network).

Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics