Groupe d’études et de recherche en analyse des décisions


A Note on the Definition of a Linear Bilevel Programming Solution

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An alternative definition of the linear bilevel programming problem BLP has recently 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 transferring 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.

, 8 pages