Regularized Primal-Dual Subgradient Method for Distributed Constrained Optimization.

Area of Science:

• Distributed Systems
• Optimization Theory
• Network Science

Background:

• Distributed constrained optimization problems are common in networked systems.
• Existing methods often require frequent projections, increasing computational cost.
• Efficiently solving these problems is crucial for various applications.

Purpose of the Study:

• To develop a novel distributed optimization method for minimizing the sum of local convex cost functions under a global inequality constraint.
• To reduce the computational burden by minimizing the number of projection operations.
• To establish the convergence properties and rate of the proposed method.

Main Methods:

• A consensus-based distributed regularized primal-dual subgradient method is proposed.
• The method incorporates a novel approach requiring only a single projection at the final iteration.
• Convergence analysis is performed to determine the method's efficiency.

Main Results:

• The proposed method achieves an O(K^(-1/4)) convergence rate for general distributed constrained optimization problems.
• It significantly reduces the number of required projection operations compared to existing techniques.
• Numerical examples validate the theoretical convergence findings.

Conclusions:

• The developed method offers an efficient and computationally less intensive solution for distributed constrained optimization.
• The reduced projection requirement makes it practical for large-scale networked systems.
• The established convergence rate provides theoretical guarantees for its performance.