Bard J. Practical Bilevel Optimization. Algorithms and Applications 1998

Textbook in PDF format

The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problem in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense.
Part I Mathematical Programming
Linear Programming
Integer Programming
Nonlinear Programming
Part II Bilevel Programming
Linear Bilevel Programming: Continuous Variables
Linear Bilevel Programming: Discrete Variables
Convex Bilevel Programming
General Bilevel Programming
Heuristics
Part III Applications
Transportation Network Design
Production Planning
Determining Price Support Levels for Biofuel Crops