Sensitivity analysis in bilevel linear programming

This paper studies sensitivity analysis of bilevel linear programming. Two cases of the leader's objective function and the right-hand side of the constraints including parameters are discussed separately. This paper also presents a necessary and sufficient optimality condition for optimal solution to a bilevel linear programming problem and its equivalent expression in nonconvex quadratic programming. The necessary and sufficient conditions are proposed to guarantee that the current optimal solution or the corresponding basis remains optimal when the parameters vary. An algorithm is also proposed to determine the set of the parameters which leaves the current optimal solution optimal or ε-optimal.