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Distributed Optimization for Second-Order Discrete-Time Multiagent Systems With Set Constraints
IEEE Transactions on Neural Networks and Learning Systems
|December 7, 2021
Summary
This study introduces a distributed optimization algorithm for multiagent systems to find optimal solutions within constrained sets. The algorithm ensures convergence to a unique solution for strongly convex problems and can be extended to convex problems.
Area of Science:
- Control Theory
- Optimization
- Distributed Systems
Background:
- Multiagent systems often face complex optimization problems with individual constraints.
- Cooperative search for a global optimum requires efficient distributed algorithms.
Purpose of the Study:
- To develop a distributed optimization algorithm for second-order discrete-time multiagent systems.
- To address cooperative optimization within the intersection of constrained sets, with private data access for each agent.
Main Methods:
- A projection-based distributed optimization algorithm using auxiliary dynamics is proposed, avoiding direct gradient sharing.
- Convergence criteria for step size and algorithm parameters are derived for strongly convex objective functions.
Main Results:
- The algorithm achieves convergence to a unique optimal solution for strongly convex local objective functions.
- The optimization result is extended to convex local objective functions with appropriate parameter selection.
Conclusions:
- The developed algorithm offers an effective approach for distributed optimization in constrained multiagent systems.
- The findings are validated through practical and numerical examples, demonstrating the algorithm's efficacy.
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