Distributed Inertial k-Winners-Take-All Neural Network Based on Quadratic Optimization Problems

The $k$ -winners-take-all ( $k$ -WTA) problem is to find the $k$ largest inputs from $n$ inputs. Based on the existing quadratic programming model, this article proposes a new $k$ -WTA network with an inertia term. The inertial term is designed to modulate the instantaneous behavior of the trajectory and use historical information to accelerate convergence. Traditional Lyapunov methods are inapplicable due to the inertia term. To overcome this, a cocoercive operator is used to prove asymptotic and exponential convergence to the $k$ -WTA solution from any initial state. Additionally, the article investigates distributed $k$ -WTA networks with restrictive equality constraints. Finally, simulations are used to confirm the efficacy of the suggested $k$ -WTA network.