Consensus-ADMM-Integrated Particle Swarm Optimization for Distributed Convex–Nonconvex Programs Over Time-Varying Graphs

• Rizky A. Pratama

  Nusantara Institute of Technology, Department of Computer Science and Intelligent Systems, Jalan Diponegoro 112, Yogyakarta 55233, Indonesia

  Author

• Siti Nurhaliza Putri

  Bandung Raya University, Faculty of Computing and Digital Media, Jalan Merdeka 45, Bandung 40115, Indonesia

  Author

Distributed optimization over multi-agent networks arises in estimation, control, and learning tasks where data is geographically dispersed and communication is constrained. Classical distributed convex optimization methods rely on strong convexity and static graph assumptions, while many emerging applications feature nonconvex local objectives and time-varying communication topologies. Metaheuristic search strategies, such as particle swarm optimization, have been used to explore complex landscapes, but they often lack a systematic treatment of consensus and dual variables. This work considers a distributed composite convex–nonconvex program defined over a network of agents connected by a time-varying graph. Each agent possesses a local cost function with both convex and nonconvex components and participates in a consensus constraint enforced through local interactions. A consensus-based alternating direction method of multipliers is integrated with a particle swarm mechanism in order to combine structured augmented Lagrangian updates with stochastic exploration in the primal domain. The resulting scheme allows each agent to maintain local primal, dual, and velocity states while exchanging low-dimensional consensus variables with neighbors. The algorithm is described in a unified operator form that highlights the interaction between consensus steps, dual ascent, and swarm-based perturbations. Conditions on the communication weights, penalty parameters, and search coefficients are discussed under which consensus is asymptotically preserved and the network trajectories approach stationary solutions of the nonconvex problem. Implementation aspects for large networks and numerical illustration scenarios are outlined to indicate how the method behaves in representative distributed optimization tasks with heterogeneous local models.

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