Discrete linear bilevel programming problem |
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| Authors: | L. Vicente G. Savard J. Judice |
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| Affiliation: | (1) Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal;(2) Present address: Department of Computational and Applied Mathematics, Rice University, Houston, Texas;(3) Département de Mathématiques et Génie Industriel, Ecole Polytechnique de Montreal, Montreal, Quebec, Canada |
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| Abstract: | In this paper, we analyze some properties of the discrete linear bilevel program for different discretizations of the set of variables. We study the geometry of the feasible set and discuss the existence of an optimal solution. We also establish equivalences between different classes of discrete linear bilevel programs and particular linear multilevel programming problems. These equivalences are based on concave penalty functions and can be used to design penalty function methods for the solution of discrete linear bilevel programs.Support of this work has been provided by the INIC (Portugal) under Contract 89/EXA/5, by INVOTAN, FLAD, and CCLA (Portugal), and by FCAR (Québec), NSERC, and DND-ARP (Canada). |
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| Keywords: | Linear bilevel programming integer linear programming exact penalty functions |
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