A simple algorithm for the simple bilevel programming (SBP) problem

In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming (SBP) problem. One of the key features of our algorithm is that we make no assumption on the diferentiability of the upper level objective, though we will assume that the lower level objective is smooth. Another key feature of the algorithm is that it does not assume that the lower level objective has a Lipschitz gradient, which is a standard assumption in most of the well-known algorithms for this class of problems. We present the convergence analysis and also some numerical experiments demonstrating the efectiveness of the algorithm.