Mathematical Programs with Equilibrium Constraints

An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.

Zhi-Quan Luo (Author), Jong-Shi Pang (Author), Daniel Ralph (Author)

9780521065085, Cambridge University Press

Paperback / softback, published 12 June 2008

428 pages, 4 tables
22.9 x 15.1 x 2.4 cm, 0.622 kg

"The book provides a good basis for further theoretical and applications-oriented investigations of MPECs. This monograph can be recommended as a valuable resource in applied mathematics, especially in the fields of operations research and engineering, as well as for specialists in mathematical prgramming." Stephen Dempe,Mathematical Reviews

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.

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.

Subject Areas: Optimization [PBU]