Abstract
In this paper a model for a two-level planning problem is presented in the form of a static Stackelberg game. By assumption, play is sequential and noncooperative; however, the leader can influence the actions of the followers through a set of coordination variables while the followers' responses may partly determine the leader's payoff.
Under certain convexity assumptions, it is shown that the feasible region induced by the leader is continuous in the original problem variables. This observation, coupled with two corollary results, are used as a basis for a hybrid algorithm which clings to the inducible region until a local optimum is found. A branching scheme is then employed to located other segments of the region, eventually terminating with the global optimum. A number of examples are given to highlight the results, while the algorithm's performance is tested in a comparison with two other procedures.
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Bard, J.F. Convex two-level optimization. Mathematical Programming 40, 15–27 (1988). https://doi.org/10.1007/BF01580720
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DOI: https://doi.org/10.1007/BF01580720