Mathematical Programs with Equilibrium Constraints

Erscheinungsjahr 2008
ISBN: 978-0-521-06508-5
Verlag: Cambridge University Press

Buch, Englisch, 428 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 691 g

This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.

Autoren/Hrsg.

Luo, Zhi-Quan

Pang, Jong-Shi

Ralph, Daniel

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung

Inhaltsverzeichnis

1. Introduction
2. Exact penalisation of MPEC
3. First-order optimality conditions
4. Verification of MPEC hypotheses
5. Second-order optimality conditions
6. Algorithms for MPEC.