Projected-Reflected Subgradient-Extragradient Method and Its Real-World Applications

Our main focus in this work is the classical variational inequality problem with Lipschitz continuous and pseudo-monotone mapping real Hilbert spaces. An adaptive reflected subgradient-extragradient method presented along its weak convergence analysis. The novelty of proposed lies fact that only one projection onto feasible set each iteration required, there no need to know/approximate constant cost function a priori. To illustrate emphasize potential applicability new scheme, several numerical experiments comparisons tomography reconstruction, Nash–Cournot oligopolistic equilibrium, more are presented.