Viscosity inexact projection methods with applications to electricity production models

In this paper, we propose a new inexact projection approach for multivalued variational inquality problems without using inertial technique in a real Hilbert space. First, we introduce a new inxact projection and show some its properties. By combining the inexact projection, viscosity technique and Mann-type iteration method via self-adaptive step size, we introduce a new VIP-Viscosity Inexact Projection Algorithm and prove its strong convergence under Lipschitz continuous and pseudomonotone assumptions of the cost multivalued mapping. Next, we apply the algorithm VIP to propose a new algorithm for the electricity production models. The effectiveness of the algorithm VIP is then validated by numerical experiments via computational examples of the electricity production models.