Augmented Cucker-Smale Model for Distributed Optimization

The Cucker-Smale (C-S) model describes an interacting particle system in which the connection weights decrease with increasing distance. This model features emergent behaviors by which the velocities of the particles converge to a common value without a central command. However, the consensus value of the original C-S flocking model is restricted to the leader-following consensus or average consensus. Moreover, for the short-range communication-based C-S model, consensus can only be obtained for specific initial configurations. In this paper, the short-range communication-based C-S model is extended to achieve distributed optimization, where the consensus value optimizes the objective function of the group for any bounded initial configuration. Simulation examples are provided to demonstrate the effectiveness of our approach.