Extragradient Methods for Vector Equilibrium Problems in Banach Spaces
Alfredo Noel Iusem, Vahid Mohebbi · Numerical Functional Analysis and Optimization · 2019
We consider the vector equilibrium problem, which extends the scalar equilibrium problem to vector valued bifunctions, in a Banach space setting. We propose an extragradient method for solving this problem. Under suitable assumptions on the bifunction, we prove that the generated sequence is weakly convergent to a solution of the problem. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.