A RNNs-based Algorithm for Decentralized-partial-consensus Constrained Optimization

TL;DR

This paper introduces a novel continuous-time algorithm based on interconnected RNNs for decentralized partial-consensus constrained optimization with inequality constraints, ensuring convergence and demonstrating effectiveness through examples.

Contribution

It develops a new RNN-based algorithm for decentralized partial-consensus optimization with inequality constraints, including convergence analysis and practical validation.

Findings

The algorithm guarantees convergence under certain conditions.

The method effectively solves decentralized partial-consensus problems.

Numerical examples demonstrate the algorithm's practical effectiveness.

Abstract

This technical note proposes the decentralized-partial-consensus optimization with inequality constraints, and a continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the obtained optimization problems. First, the partial-consensus matrix originating from Laplacian matrix is constructed to tackle the partial-consensus constraints. In addition, using the non-smooth analysis and Lyapunov-based technique, the convergence property about the designed algorithm is further guaranteed. Finally, the effectiveness of the obtained results is shown while several examples are presented.