Distributed Gradient Method for Neural Network-Based Constrained κ-Winners-Take-All

Thispaper studies the neural network-based distributed constrained κ-winners-take-all (κWTA) problem, which aims to select κ largest inputs from amount of inputs under two types of global coupled constraints. Namely, equality and inequality constrained κWTA problems. By selecting the proper parameter, the two constrained κWTA problems can be transformed into two continuous constrained quadratic programming problems. Subsequently, we propose a derivative feedback-based modified primal-dual fully distributed algorithm for the κWTA problem with a global coupled equality constraint by utilizing Karush-Kuhn-Tucker (KKT) conditions and the gradient flow method. In addition, the developed derivative feedback-based distributed neurodynamic method is initialization-free. Furthermore, the above method is revised via a maximal projection operator for the κWTA problem with a global coupled inequality constraint. The two methods are rigorously proved to asymptotically solve the distributed constrained κWTA models in accordance with LaSalle's invariance principle. The performance of our designed methods is tested via four simulation examples.