Linear bilevel problems: Genericity results and an efficient method for computing local minima

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no theoretically efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for efficiently computing local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps.