A simple algorithm for the-linear bilevel programming problem

Abstract

In the Paper an algorithm for the linear bilevel programming problem is offered which applies mainly the ususal simplex method with and additional rule for including slack variables into the basis. The algorithm bases on the full description of the feasible set in a neighbourhood of a feasible point. This description is obtained using the theory of subradients as well as the concept of “active constraints”. The result is an algorithm which seems to be easier to implement as other published procedures also based on theorem that every solvable linear bilevel programming problem has a basic solution.