A neural network method for solving a system of linear variational inequalities

Discrete-time projection neural network methods for computing the solution of variational inequalities

“…Most recently, Lan and Cui [10] investigated the neural network method for solving the following variational inequalities: find (x, y) ∈ Ω 1 × Ω 2 such that (α − x) (x − y + Ny + p) 0, ∀α ∈ Ω 1 , (β − y) (y − x + Mx + q) 0, ∀β ∈ Ω 2 , (…”

“…We note that the variational inequalities (1.2) have numerous applications such as economic equilibrium modeling, traffic networks equilibrium modeling, and structural analysis; see, for example [4,6]. In [10], the authors transmuted the solution of (1.2) to an equilibrium point of neural networks and analyzed the stability and convergence rate of the neural networks. The results presented in [10] generalize and improve the existing works in the literature.…”

“…In [10], the authors transmuted the solution of (1.2) to an equilibrium point of neural networks and analyzed the stability and convergence rate of the neural networks. The results presented in [10] generalize and improve the existing works in the literature. While most neural networks mentioned above are studied in continuous-time level, there exist at least two aspects that make the analysis of the discrete-time analogues important.…”

“…We utilize the implicit-explicit-θ (IMEX-θ) method and the one proposed by Mohamad et al [5,14,15,[17][18][19] to discretize the continuous-time neural networks introduced in [10], and then by using Lyapunov function and Razumikhin-type techniques we investigate exponential stability of the derived discrete-time analogues. The sufficient stability criteria are established in terms of linear matrix inequalities (LMIs), which can be solved numerically and very efficiently using the interior point algorithms [2].…”