Foundations of Bilevel Programming

Stephan Dempe

ISBN 10: 1441952209 / ISBN 13: 9781441952202

Verlag: Springer US, Springer US Dez 2010, 2010

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 320 pp. Englisch.

Bestandsnummer des Verkäufers 9781441952202

Bibliografische Details

• Titel: Foundations of Bilevel Programming
• Verlag: Springer US, Springer US Dez 2010
• Veröffentlichungsdatum: 2010
• Sprache: Englisch
• ISBN-10: 1441952209
• ISBN-13: 9781441952202
• Bindung: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.