An extended Kuhn–Tucker approach for linear bilevel programming

Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principal challenge is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of arbitrary linear form. This paper describes theoretical foundation of Kuhn–Tucker approach and proposes an extended Kuhn–Tucker approach to deal with the problem. The results have demonstrated that the extended Kuhn–Tucker approach can solve a wider class of linear BLP problems than current capabilities permit.