A note on the definition of a linear bilevel programming solution Charles Audet 1,2 , Jean Haddad 2 , Gilles Savard 1,2 Abstract An alternative definition of the linear bilevel programming problem BLP has re- cently been proposed by Lu, Shi, and Zhang. This note shows that the proposed definition is a restriction of BLP . Indeed, the new definition is equivalent to trans- ferring the first-level constraints involving second-level variables into the second level, resulting in a special case of BLP in which there are no first-level constraint involving second-level variables. Thus, contrary to what is stated by the authors who suggested the new definition, this does not allow to solve a wider class of problems, but rather relaxes the feasible region, allowing for infeasible points to be considered as feasible. Key words: Optimization, Linear bilevel programming 1 Introduction The aim of this note is to show that the deficiency pointed out in [8,9,10] is not really a deficiency and that the new definition proposed is equivalent to moving the first-level constraints involving the second-level variables into the second level, which changes the nature of the problem. A bilevel program is a program in which a subset of the variables is required to be an optimal solution of a second mathematical program [1,2,3,5,6,7,12]. The linear bilevel program is a special case in which all the constraints and the Email addresses: Charles.Audet@gerad.ca (Charles Audet ), Jean.Haddad@polymtl.ca (Jean Haddad), Gilles.Savard@gerad.ca (Gilles Savard). URL: http://www.gerad.ca/Charles.Audet (Charles Audet ). 1 GERAD 2 D´ epartement de Math´ ematique et de G´ enie Industriel, ´ Ecole Polytechnique de Montr´ eal, C.P. 6079, succ. Centre-ville, Montr´ eal (Qu´ ebec), H3C 3A7 Canada Preprint submitted to Elsevier Science 3rd October 2005