Bilevel programming problems are hierarchical optimization problems
where the constraints of one problem (the so-called upper level
problem) are defined in part by a second parametric optimization
problem (the lower level problem). If the lower level problem has a
unique optimal solution for all parameter values, this problem is
equivalent to a one-level optimization problem having an implicitly
defined objective function. Special emphasize in the book is on
problems having non-unique lower level optimal solutions, the
optimistic (or weak) and the pessimistic (or strong) approaches are
discussed. The book starts with the required results in parametric
nonlinear optimization. This is followed by the main theoretical
results including necessary and sufficient optimality conditions
and solution algorithms for bilevel problems. Stationarity
conditions can be applied to the lower level problem to transform
the optimistic bilevel programming problem into a one-level
problem. Properties of the resulting problem are highlighted and
its relation to the bilevel problem is investigated. Stability
properties, numerical complexity, and problems having additional
integrality conditions on the variables are also discussed.
Audience: Applied mathematicians and economists working in
optimization, operations research, and economic modelling. Students
interested in optimization will also find this book useful.
General
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