Projection algorithms with adaptive step sizes for multiple output split mixed variational inequality problems

We present new iterative algorithms for solving a split convex feasibility problem with multiple output sets involving a monotone mixed variational inequality in real Hilbert spaces. The proposed algorithms follow the Tseng projection method, but with self-adaptive step-sizes that do not depend on the norm of the transfer operator as well as knowledge of a Lipschitz constant. The convergence of the sequences generated by the proposed algorithms is established. We use the proposed algorithms to solve a modified oligopolistic Nash–Cournot equilibrium model. Numerical experiments show that our algorithms are efficient and competitive compared to several recent algorithms.