Distributed Randomized Gradient-Free Optimization Protocol of Multiagent Systems Over Weight-Unbalanced Digraphs

Area of Science:

• Distributed optimization
• Multiagent systems
• Convex optimization

Background:

• Distributed constrained convex optimization is crucial for multiagent systems.
• Existing methods often require diminishing step sizes or specific network structures.

Purpose of the Study:

• To propose a distributed randomized gradient-free optimization protocol for multiagent systems.
• To address optimization problems over weight-unbalanced directed graphs.

Main Methods:

• Utilizing a gradient-free approach with local nonsmooth, Lipschitz continuous objective functions.
• Implementing a protocol where agents update states based on in-neighbor information over row-stochastic matrices.
• Relaxing diminishing step size requirements to a nonsummable condition.

Main Results:

• The proposed algorithm demonstrates consistency and convergence under relaxed step size conditions.
• Convergence rates are analyzed and shown for various step sizes.
• The method is applicable to weight-unbalanced directed graphs.

Conclusions:

• The developed gradient-free protocol offers a flexible and implementable solution for distributed optimization in multiagent systems.
• The theoretical analysis, utilizing boundedness and ultimate limits, validates the algorithm's performance.
• Numerical examples confirm the practical effectiveness of the proposed approach.