A SOLUTION METHOD FOR THE STATIC CONSTRAINED STACKELBERG PROBLEM VIA PENALTY METHOD

A new solution method for the static constrained Stackelberg problem is presented. Through this 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 respect to the leader's and the follower's variables jointly. It is proved that, when the penalty parameters are updated, a sequence of solutions to the transformed problems converges to the solution of the original problem. These computational experiments confirm the convergence property and availability of the method. However, computational difficulties of ill-conditioning in the vicinity of the boundary of the feasible region arise when r and t are too small and s is too large.