Mathematical Programs with Equilibrium Constraints
Mathematical Programs with Equilibrium Constraints by Zhi-Quan Luo, published by Cambridge University Press on June 12, 2008, is a comprehensive resource that delves into the study of Mathematical Programs with Equilibrium Constraints (MPEC). Spanning 428 pages, this book lays a solid foundation for understanding various source problems in engineering and economics that can be effectively addressed using the MPEC methodology.
Readers will find an in-depth exploration of key concepts such as error bounds and parametric analysis, which are essential for establishing a theory of exact penalization. The book also outlines several iterative algorithms, including a penalty-based interior point algorithm and an implicit programming algorithm, tailored for MPECs. The results presented are relevant to fields like engineering design, economics, and transportation planning, highlighting the significant role of MPEC in modeling practical problems across these disciplines.
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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