A solution method for the static constrained Stackelberg problem via penalty method

Abstract

This note presents a new solution method for the static constrained Stackelberg problem. Through our approach, the Stackelberg problem is completely transformed into a one-level unconstrained problem such that the newly introduced overall augmented objective function is minimized with repect to the leader's and the follower's variables jointly. It can be proved that a sequence of solutions to the transformed problems converges to the solution of the original problem, when the penalty parameters are updated.