A novel distributed gradient algorithm for composite constrained optimization over directed network.

Area of Science:

• Optimization Theory
• Distributed Systems
• Convex Analysis

Background:

• Constrained convex optimization problems are prevalent in fields like power allocation and sensor networks.
• Existing methods often struggle with distributed settings and specific constraint types.
• The [Formula: see text] norm is a common regularization component in these problems.

Purpose of the Study:

• To develop a novel distributed optimization algorithm for a specific class of constrained convex problems.
• To address challenges in directed communication networks without requiring full neighbor information.
• To ensure convergence guarantees under specified conditions.

Main Methods:

• A new distributed optimization approach using a time-varying, constant step-size mechanism.
• Utilization of row-stochastic weight matrices for network communication.
• Theoretical analysis based on convexity and Lipschitz continuity of local objectives.

Main Results:

• The proposed method converges to the optimal point under defined step-size and objective function constraints.
• The approach effectively handles constrained optimization over directed communication networks.
• Simulation experiments confirm the method's efficiency and applicability.

Conclusions:

• The developed distributed optimization method offers an efficient and robust solution for constrained convex problems.
• The technique is applicable to real-world scenarios such as power allocation and network coordination.
• The theoretical guarantees and simulation results validate the proposed algorithm's performance.