convergence rate

variational inequalities

nonexpansive mappings

strong convergence

vector equilibrium

ill-posed problems

variational inequality

conjugate gradient

Applicable analysis

In this paper, we introduce a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. We prove a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Moreover, we apply our results to approximate solution of convex minimization problem, and we present some numerical experiments to show the efficiency and applicability of our method in comparison with some existing methods in the literature. Our proposed method is easy to implement. It requires only one projection onto a constructible half-space.

Relaxed inertial Tseng extragradient method for variational inequality and fixed point problems