Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 217, Issue 15, Pages 6680-6690Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.01.066
Keywords
Sequential quadratic programming algorithm; Convex bilevel problem; Complementary constraints; Inducible solution; Semismooth equations; Smoothing method
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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. (C) 2011 Elsevier Inc. All rights reserved.
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