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

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2 Author(s)
Anandalingam, G. ; Dept. of Syst., Pennsylvania Univ., Philadelphia, PA, USA ; White, D.J.

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

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Automatic Control, IEEE Transactions on  (Volume:35 ,  Issue: 10 )