  We consider a scalar objective minimization problem over the solution set of
another optimization problem. This problem is known as simple bilevel
optimization problem and has drawn a significant attention in the last few
years. Our inner problem consists of minimizing the sum of smooth and nonsmooth
functions while the outer one is the minimization of a smooth convex function.
We propose and establish the convergence of a fixed-point iterative method with
inertial extrapolation to solve the problem. Our numerical experiments show
that the method proposed in this paper outperforms the currently best known
algorithm to solve the class of problem considered.
