A Fixed Step-Size Algorithm for Distributed Optimization With Both Globally Coupled and Locally Separated...

Area of Science:

• Distributed Optimization
• Multiagent Systems
• Control Theory

Background:

• Multiagent systems face challenges in optimizing cooperative tasks with globally coupled constraints.
• Existing methods may struggle with scalability and convergence in complex networks.

Purpose of the Study:

• To propose a novel distributed algorithm for constrained optimization in multiagent networks.
• To address the challenge of globally coupled constraints using multiplier estimations.
• To ensure convergence and demonstrate practical applicability.

Main Methods:

• Developed a distributed Lagrange alternating gradient descent (LAGD) algorithm with a fixed step size.
• Agents cooperatively optimize local objectives under local constraints.
• Utilized network communication for consensus on multiplier estimations to handle global constraints.

Main Results:

• The LAGD algorithm achieves convergence to the optimal solution for decision variables.
• Convergence is proven under fixed step sizes with a theoretical upper bound.
• Demonstrated effectiveness through an economic dispatch problem in a power system.

Conclusions:

• The proposed distributed LAGD algorithm effectively solves constrained optimization problems in multiagent networks.
• The algorithm's convergence properties are theoretically established.
• Practical validation confirms its utility in real-world applications like power systems.