An algorithm for the problem of bilevel programming

In this work, we present a feasible descent algorithm for the Bilevel Programming Problem (BLPP). In general, this problem is constrained, nondifferentiable and nonconvex. The proposed algorithm considers a sequence of nondifferentiable problems, where the feasible set is a perturbation of the feasible set of the original problem. Using the Method of Centers, we determine a stationary point for each perturbed problem. Thus, we get a feasible minimization sequence for the BLPP (feasible in the sense that it belongs to the constraints region of the BLPP). We analyze the convergence and establish that, when the perturbation tends to zero, any cluster point of the generated sequence is a stationary point of the original problem. We finish the work with some numerical examples.