<i>k</i> -Winner-Take-All Competition Based on Novel Dynamic Neural Networks

Thek-winner-takes-all (k-WTA) problem involves selecting the topkagents with the highest inputs from a set ofncandidates. This problem plays a fundamental role in modeling competitive behaviors in social systems and economic environments. In this article, we propose a structurally simplified dynamic neural network to solve thek-WTA problem efficiently. The originalk-WTA task is first reformulated as a constrained quadratic programming (QP) problem. A smooth sigmoid function is then introduced to encode inequality constraints implicitly, simplifying the representation. Based on this formulation, we develop a continuous-time neural dynamic model capable of solving the problem in real time. The proposed model is theoretically proven to achieve global convergence and optimality with respect to thek-WTA solution. Extensive numerical experiments, including tests on real-world data, validate the effectiveness of the proposed approach, demonstrating fast convergence, robustness, and practical applicability.