Optimality conditions and an algorithm for linear-quadratic bilevel programs. (English) Zbl 0819.90106
Summary: We study linear-quadratic bilevel programming. Several necessary and/or sufficient optimality conditions for a linear-quadratic bilevel program are derived 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.
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