Follower Cooperation Research Articles

A new method for strong-weak linear bilevel programming problem

We first propose an exact penalty method to solve strong-weak linearbilevel programming problem (for short, SWLBP) for every fixedcooperation degree from the follower. Then, we prove that the solution ofpenalized problem is also that of the original problem under someconditions. Furthermore, we give some properties of the optimalvalue function (as a function of the follower's cooperation degree)of SWLBP. Finally, we develop a method to acquire the criticalpoints of the optimal value function without enumerating all valuesof the cooperation degree from the follower, and thus this functionis also achieved. Numerical results show that the proposedmethods are feasible.

New partial cooperation model for bilevel programming problems

Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower's optimal reaction is not unique. However, in these existed models, the follower's cooperation level does not depend on the leader's decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semicontinuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and non-lower semi-continuous.