Mathematical Programs with Equilibrium Constraints

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Cambridge University Press, Nov 13, 1996 - Mathematics - 401 pages
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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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Exact Penalization of MPEC
FirstOrder Optimality Conditions
Verification of MPEC Hypotheses
SecondOrder Optimality Conditions
Algorithms for MPEC

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About the author (1996)

Zhi-Quan (Tom) Luo is a Professor at the University of Minnesota. He has served as the Editor-in-Chief of IEEE Transactions on Signal Processing and is a Fellow of the IEEE, SIAM, and the Royal Society of Canada.

Jong-Shi Pang is the Caterpillar Professor and Head of the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign. He won the 2003 George B. Dantzig Prize awarded jointly by the Mathematical Programming Society and SIAM for his work on finite-dimensional variational inequalities.

Daniel Ralph is an engineering manager at Btexact Technologies, where he is responsible for a number of projects in the mobile applications arena. He currently consults and project-manages application development, application integration and systems migration, and is also interested in the wider commercial, social and political implications association with the impact of knowledge society.
Daniel received his masters degree in Telecommunications Engineering at University College London. He also holds a BSc(Hons) in Computer Science from the Open University. He is a member of the British Computer Society and is a chartered engineer. He has authored a number of journal papers and presented at conferences on the subject of delivering services via mobility portal and technologies of the mobile internet.

Paul Graham is an engineering manager at eServGlobal, where he is responsible for a number of projects associated with the development of Intelligent Network Services and mobile applications.
Paul received his master's degree in Telecommunications Technology at Aston University. He also holds a BEng in Electronics from Southampton University. He is a member of the IEE and has vast experience in the telecommunications industry, having served three years at BT's research facility at Martlesham Health (near Ipswich), followed by five years working for G8 Labs/eServGlobal. This includes periods working for Stratus, Ascend and Lucent Technologies in the USA and throughout Europe. His current interests include next-generation Internet services and mobile services. He specializes in billing systems and data services.

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