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.
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