Distributed nonconvex optimization subject to globally coupled constraints via collaborative neurodynamic...

Area of Science:

• Optimization Theory
• Artificial Intelligence
• Distributed Systems

Background:

• Nonconvex optimization problems with coupled and local constraints are prevalent in various fields.
• Existing methods often struggle with the complexity and distributed nature of these problems.
• Developing efficient algorithms for nonconvex distributed optimization remains a significant challenge.

Purpose of the Study:

• To propose a novel recurrent neural network (RNN) for solving distributed nonconvex optimization problems.
• To address challenges posed by globally coupled (in)equality constraints and local bound constraints.
• To develop methods for both local and global optimal solution searches.

Main Methods:

• Design of an augmented Lagrangian function to handle nonconvexity.
• Development of a distributed recurrent neural network for optimization.
• Establishment of a collaborative neurodynamic optimization method using multiple RNNs and meta-heuristics.
• Proof of convergence to a local optimal solution for the proposed RNN.

Main Results:

• The proposed RNN effectively solves distributed nonconvex optimization problems.
• Convergence to a local optimal solution is mathematically proven.
• The collaborative method demonstrates potential for finding global optimal solutions.
• Numerical examples, including an electricity market simulation and a control problem, validate the approach.

Conclusions:

• The developed recurrent neural network offers a robust solution for distributed nonconvex optimization.
• The collaborative neurodynamic approach enhances the capability to find global optima.
• The findings have practical implications for resource allocation, market simulations, and cooperative control systems.