Optimality conditions and an algorithm for linear-quadratic bilevel programs$fr1:1$f:1partially supported by nsfc and madis. this paper was prepared during the first author's visiting universitat de barcelona. he is grateful to the financial support provided by universitat de barcelona. the authors are very grateful to the referees for their valuable suggestions and comments

In this paper. We study linear-quadratic bilevel programming. Several necessary and/or sufficient optimality conditions for a linear-quadratic bilevel program are derived based on the Kuhn-Tucker condition and the duality theory. It is proved that the original linear-quadratic bilevel program can be solved by solving a standard linear program and the optimal objective value of the original problem can be achieved at some extreme point of a newly constructed polyhedral convex set. According to the theory developed in this paper we propose an algorithm to solve linear-quadratic bilevel programming problems. Some numerical results are also given to illustrate the algorithm