Distributed Nesterov Gradient and Heavy-Ball Double Accelerated Asynchronous Optimization.

Area of Science:

• Optimization Algorithms
• Distributed Systems
• Networked Control

Background:

• Distributed optimization problems involve agents minimizing a sum of local objectives.
• Existing methods often require synchronous communication, limiting practical application.
• Handling asynchronous communication and unpredictable delays is a key challenge.

Purpose of the Study:

• To develop novel accelerated distributed optimization algorithms.
• To address challenges posed by asynchronous communication and time-varying delays.
• To achieve efficient and robust distributed optimization over directed graphs.

Main Methods:

• Developed a novel Nesterov gradient and heavy-ball double accelerated synchronous algorithm (NHDA).
• Proposed an asynchronous algorithm (ASY-NHDA) by transforming the asynchronous system into an augmented synchronous system.
• Utilized consensus, gradient tracking, and generalized small gain theorem for theoretical analysis.

Main Results:

• Both NHDA and ASY-NHDA algorithms demonstrate linear convergence to the optimal solution.
• Convergence is achieved under specific bounds for step size and momentum parameters.
• ASY-NHDA shows advantages in simulations, effectively managing asynchronous operations.

Conclusions:

• The proposed NHDA and ASY-NHDA algorithms offer efficient solutions for distributed optimization.
• ASY-NHDA provides a robust approach for systems with arbitrary, time-varying delays.
• These algorithms advance the field of distributed optimization for networked systems.