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
