Using laplacian eigenmap as heuristic information to solve nonlinear constraints defined on a graph and its application in distributed range-free localization of wireless sensor networks

In this paper, we are concerned with the problem of nonlinear inequalities defined on a graph. The feasible solution set to this problem is often infinity and Laplacian eigenmap is used as heuristic information to gain better performance in the solution. A continuous-time projected neural network, and the corresponding discrete-time projected neural network are both given to tackle this problem iteratively. The convergence of the neural networks are proven in theory. The effectiveness of the proposed neural networks are tested and compared with others via its applications in the range-free localization of wireless sensor networks. Simulations demonstrate the effectiveness of the proposed methods.