Mathematical Programs with Equilibrium Constraints
Mathematical Programs with Equilibrium Constraints by Zhi-Quan Luo, published by Cambridge University Press on November 13, 1996, spans 401 pages and is presented in English. This book provides a solid foundation and an extensive study of Mathematical Programs with Equilibrium Constraints (MPEC), beginning with a description of various source problems from engineering and economics that can be addressed using the MPEC methodology.
Readers will find a thorough exploration of error bounds and parametric analysis, which are essential for establishing a theory of exact penalization, along with MPEC constraint qualifications and optimality conditions. The book also details several iterative algorithms, including a penalty-based interior point algorithm and a piecewise sequential quadratic programming algorithm for MPECs. The results discussed are anticipated to influence fields such as engineering design, economics, and transportation planning, highlighting the central role of MPEC in modeling practical problems.
Official synopsis Publisher
This book provides a solid foundation and an extensive study for Mathematical Programs with Equilibrium Constraints (MPEC). It 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 penalization, 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 modeling of many practical problems.
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