Solving quadratic convex bilevel programming problems using a smoothing method |
| |
Authors: | Jean Bosco Etoa Etoa |
| |
Affiliation: | Department of Management and Economic Sciences, University of Yaounde II, BP15 Soa, Cameroon |
| |
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. |
| |
Keywords: | Sequential quadratic programming algorithm Convex bilevel problem Complementary constraints Inducible solution Semismooth equations Smoothing method |
本文献已被 ScienceDirect 等数据库收录! |
|