Solving quadratic convex bilevel programming problems using a smoothing method (Q632921)

A smoothing sequential quadratic programming method is proposed for solving a quadratic convex bilevel programming problem. The Karush-Kuhn-Tucker optimality conditions of the lower level problem are used to obtain a nonsmooth optimization problem known to be a mathematical programming problem with equilibrium constraints. The complementarity conditions of the lower problem are then appended to the upper level objective function with a classical penalty. Preliminary numerical results reported in the concluding part of the paper show efficiency of the proposed approach.