Distributed neurodynamic approaches to nonsmooth optimization problems with inequality and set constraints

In this paper, neurodynamic approaches are proposed for solving nonsmooth distributed optimization problems under inequality and set constraints, that is to find the solution that minimizes the sum of local cost functions. A continuous-time neurodynamic approach is designed and its state solution exists globally and converges to an optimal solution of the corresponding distributed optimization problem. Then, a neurodynamic approach with event-triggered mechanism is considered for the purpose of saving communication costs, and then, the convergence and its Zeno-free property are proved. Moreover, to realize the practical application of the neurodynamic approach, a discrete-time neurodynamic approach is proposed to solve nonsmooth distributed optimization problems under inequality and set constraints. It is rigorously proved that the iterative sequence generated by the discrete-time neurodynamic approach converges to the optimal solution set of the distributed optimization problem. Finally, numerical examples are solved to demonstrate the effectiveness of the proposed neurodynamic approaches, and the neurodynamic approach is further applied to solve the ill-conditioned Least Absolute Deviation problem and the load sharing optimization problem.