Feasible direction method for bilevel programming problem

Abstract

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.

Keywords:

• nonlinear programming
• bilevel programming
• solution algorithm
• Bouligand stationary solution

Acknowledgements

The authors would like to thank the anonymous referee whose constructive suggestions have vastly improved the presentation of this article. Work of A.G. Mersha author was supported by DAAD (Deutscher Akademischer Austausch Dienst) with a scholarship grant.