Solving quadratic convex bilevel programming problems using a smoothing method

Solving quadratic convex bilevel programming problems using a smoothing method

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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:
Keywords: multi-level programming, sequential analysis, smoothing
Abstract:

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.

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