Foundations of Bilevel Programming

Bilevel programming problems are hierarchical optimization problems where theconstraints of one problem the socalled upper level problem are defined inpart by a... » 

Bilevel programming problems are hierarchical optimization problems where theconstraints of one problem the socalled upper level problem are defined inpart by a second parametric optimization problem the lower level problem. Ifthe lower level problem has a unique optimal solution for all parameter valuesthis problem is equivalent to a onelevel optimization problem having animplicitly defined objective function. Special emphasize in the book is onproblems having nonunique lower level optimal solutions the optimistic orweak and the pessimistic or strong approaches are discussed. The book startswith the required results in parametric nonlinear optimization. This isfollowed by the main theoretical results including necessary and sufficientoptimality conditions and solution algorithms for bilevel problems.Stationarity conditions can be applied to the lower level problem to transformthe optimistic bilevel programming problem into a onelevel problem. Propertiesof the resulting problem are highlighted and its relation to the bilevelproblem is investigated. Stability properties numerical complexity andproblems having additional integrality conditions on the variables are alsodiscussed. Audience Applied mathematicians and economists working inoptimization operations research and economic modelling. Students interestedin optimization will also find this book useful. «