A solution method for the linear static Stackelberg problem using penalty functions

A new solution technique is presented for the linear constrained static Stackelberg problem. For a given value of x, the leader´s decision vector, the follower is at its rational reaction set when the duality gap of the second-level problem becomes zero. The outer problem is solved by appending to the leader´s objective, a function that minimizes the duality gap of the follower´s problem. This structure leads to the decomposition of the composite problem into a series of linear programs leading to an efficient algorithm. It is proved that optimality is reached for an exact penalty function, and the method is illustrated with some examples