A new result for projection neural networks to solve linear variational inequalities and related optimization problems
In recent years, a projection neural network was proposed for solving linear variational inequality (LVI) problems and related optimization problems, which required the monotonicity of LVI to guarantee its convergence to the optimal solution. In this paper, we present a new result on the global exponential convergence of the projection neural network. Unlike existing convergence results for the projection neural network, our main result does not assume the monotonicity of LVI problems. Therefore, the projection neural network can be further guaranteed to solve a class of non-monotone LVI and non-convex optimization problems. Numerical examples illustrate the effectiveness of the obtained result.
projection neural network global exponential convergence non-convex optimization non-monotone linear variational inequality