Feasible direction method for bilevel programming problem

In this article, we investigate the application of feasible direction method for an optimistic non-linear bilevel programming problem. The convex lower level problem of an optimistic non-linear bilevel programming problem is replaced by relaxed KKT conditions. The feasible direction method developed by Topkis and Veinott [D. M. Topkis and A. F. jun. Veinott, On the convergence of some feasible direction algorithms for nonlinear programming, SIAM J. Control Optim. 5(1967), pp. 268-279] is applied to the auxiliary problem to get a Bouligand stationary point for an optimistic bilevel programming problem.