Extragradient Methods for Vector Equilibrium Problems in Banach Spaces. (4th July 2019) - Iusem, Alfredo N.; Mohebbi, Vahid
Abstract: 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.