An interior point technique for solving bilevel programming problems |
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Authors: | José Herskovits Mario Tanaka Filho Anatoli Leontiev |
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Affiliation: | 1. Mechanical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68503, CEP 21945-970, CT, Cidade Universitária, Ilha do Fund?o, Rio de Janeiro, Brazil 2. Mathematical Program—UFOPA, Federal University of West of Pará, Santarém, PA, Brazil 3. Instituto de Matemática, Federal University of Rio de Janeiro, Cidade Universitária, Ilha do Fund?o, CEP 21945-970, P.O. Box 68503, Rio de Janeiro, Brazil
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Abstract: | This paper deals with bilevel programs with strictly convex lower level problems. We present the theoretical basis of a kind of necessary and sufficient optimality conditions that involve a single-level mathematical program satisfying the linear independence constraint qualification. These conditions are obtained by replacing the inner problem by their optimality conditions and relaxing their inequality constraints. An algorithm for the bilevel program, based on a well known technique for classical smooth constrained optimization, is also studied. The algorithm obtains a solution of this problem with an effort similar to that required by a classical well-behaved nonlinear constrained optimization problem. Several illustrative problems which include linear, quadratic and general nonlinear functions and constraints are solved, and very good results are obtained for all cases. |
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