Distributed k-Winners-Take-All Network: An Optimization Perspective
将k胜者全取问题转化为带图拉普拉斯矩阵的约束优化问题，设计分布式投影神经网络求解，理论证明全局渐近稳定且收敛到正确解，仿真验证了有效性。
In this article, we proposed an equivalent formulation of the k-winners-take-all (k-WTA) problem as a constrained optimization problem by including the Laplacian matrix of the undirected connected communication graph to adapt to the distributed computing scenario, where an additional auxiliary variable is introduced. To solve the optimization problem in a distributed fashion, we design projection neural networks by using the convex optimization theory, leading to the emergence of a distributed k-WTA network. Our theoretical analysis shows that the proposed distributed k-WTA network has a globally asymptotically stable equilibrium that is identical to the optimal solution to the optimization problem, that is, the correct k-WTA solution. The effectiveness and advantages, including the extendability to constrained k-WTA problems, of the proposed k-WTA network are demonstrated via simulations.