• Jonathan F. Bard
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 30)


The central focus of this book is on the development and implementation of algorithms for solving bilevel programs. The bilevel programming problem (BLPP) can be viewed as a static version of the noncooperative, two—person game introduced by Von Stackelberg [S16] in the context of unbalanced economic markets. In the basic model, control of the decision variables is partitioned amongst the players who seek to optimize their individual payoff functions. Perfect information is assumed so that both players know the objective and feasible choices available to the other. The fact that the game is said to be ‘static’ implies that each player has only one move. The leader goes first and attempts to minimize net costs. In so doing, he must anticipate all possible responses of his opponent, termed the follower. The follower observes the leader’s decision and reacts in a way that is personally optimal without regard to extramural effects. Because the set of feasible choices available to either player is interdependent, the leader’s decision affects both the follower’s payoff and allowable actions, and vice versa.


Bilevel Programming Bilevel Programming Model Multilevel Programming External Diseconomy Bilevel Formulation 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Jonathan F. Bard
    • 1
  1. 1.Graduate Program in Operations Research, Department of Mechanical EngineeringThe University of TexasAustinUSA

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