Article ID: | iaor20113588 |
Volume: | 217 |
Issue: | 15 |
Start Page Number: | 6680 |
End Page Number: | 6690 |
Publication Date: | Apr 2011 |
Journal: | Applied Mathematics and Computation |
Authors: | Etoa Etoa Jean Bosco |
Keywords: | multi-level programming, sequential analysis, smoothing |
In this paper, we present a smoothing sequential quadratic programming to compute a solution of a quadratic convex bilevel programming problem. We use the Karush–Kuhn–Tucker optimality conditions of the lower level problem to obtain a nonsmooth optimization problem known to be a mathematical program with equilibrium constraints; the complementary conditions of the lower level problem are then appended to the upper level objective function with a classical penalty. These complementarity conditions are not relaxed from the constraints and they are reformulated as a system of smooth equations by mean of semismooth equations using Fisher–Burmeister functional. Then, using a quadratic sequential programming method, we solve a series of smooth, regular problems that progressively approximate the nonsmooth problem. Some preliminary computational results are reported, showing that our approach is efficient.