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.

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.

Utilising both key mathematical tools and state-of-the-art research results, this text explores the principles underpinning large-scale information processing over networks and examines the crucial interaction between big data and its associated communication, social and biological networks. Written by experts in the diverse fields of machine learning, optimisation, statistics, signal processing, networking, communications, sociology and biology, this book employs two complementary approaches: first analysing how the underlying network constrains the upper-layer of collaborative big data processing, and second, examining how big data processing may boost performance in various networks. Unifying the broad scope of the book is the rigorous mathematical treatment of the subjects, which is enriched by in-depth discussion of future directions and numerous open-ended problems that conclude each chapter. Readers will be able to master the fundamental principles for dealing with big data over large systems, making it essential reading for graduate students, scientific researchers and industry practitioners alike.