A solution method for the linear static Stackelberg problem using penalty functions
- 1 January 1990
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 35 (10) , 1170-1173
- https://doi.org/10.1109/9.58565
Abstract
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.Keywords
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