  This paper deals with the solving of variational inequality problem where the
constrained set is given as the intersection of a number of fixed-point sets.
To this end, we present an extrapolated sequential constraint method. At each
iteration, the proposed method is updated based on the ideas of a hybrid
conjugate gradient method used to accelerate the well-known hybrid steepest
descent method, and an extrapolated cyclic cutter method for solving a common
fixed point problem. We prove strong convergence of the method under some
suitable assumptions of step-size sequences. We finally show the numerical
efficiency of the proposed method compared to some existing methods.
