An Interior Point Technique for Solving Bilevel Programming Problems

This paper deals with bilevel programming programs with convex lower level problems. New necessary and sufficient optimality conditions that involve a single-level mathematical program satisfying the linear independence constraint qualification are introduced. These conditions are solved by an interior point technique for nonlinear programming. Neither the optimality conditions nor the algorithm involve any penalization and we get a solution of the bilevel program with an effort similar to that required by a classical well-behaved nonlinear constrained optimization problem. Several illustrative problems which include linear, quadratic and general nonlinear functions and constraints are solved, and very good results are obtained for all cases.