A collective neurodynamic penalty approach to nonconvex distributed constrained optimization

Area of Science:

• Distributed Optimization
• Artificial Neural Networks
• Multi-Agent Systems
• Nonconvex Optimization

Background:

• Distributed optimization problems in multi-agent networks often involve complex, nonconvex objective functions and constraints.
• Agents typically possess only local information, limiting their ability to solve global optimization tasks.
• Existing methods struggle with the inherent challenges posed by nonconvexity in distributed settings.

Purpose of the Study:

• To develop a robust method for solving nonconvex distributed optimization problems in undirected multi-agent networks.
• To address the limitations of local information access by agents.
• To achieve convergence to the globally optimal solution despite nonconvexities.

Main Methods:

• A collective neurodynamic penalty approach is proposed within the particle swarm optimization (PSO) framework.
• Each agent utilizes its individual neurodynamic model for constrained local searches.
• The approach leverages both locally best-known and globally best-known solution information for iterative improvement.

Main Results:

• The proposed neurodynamic penalty approach ensures state solution convergence towards the critical point ensemble of the nonconvex problem.
• Individual neural networks perform accurate local searches, respecting constraints.
• The iterative enhancement of solution quality leads to the identification of the globally optimal solution.

Conclusions:

• The collective neurodynamic penalty approach effectively solves nonconvex distributed optimization problems in multi-agent systems.
• The method demonstrates feasibility and effectiveness through simulations and a practical application.
• This approach offers a promising solution for complex optimization tasks in decentralized environments.