  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.
