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Mathematical Programs with Equilibrium Constraints
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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.Abstract:
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.read more
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Journal ArticleDOI
An overview of bilevel optimization
TL;DR: This paper presents fields of application, focus on solution approaches, and makes the connection with MPECs (Mathematical Programs with Equilibrium Constraints), a branch of mathematical programming of both practical and theoretical interest.
Journal ArticleDOI
Engineering and Economic Applications of Complementarity Problems
Michael C. Ferris,Jong-Shi Pang +1 more
TL;DR: The goal of this documentation is to summarize the essential applications of the nonlinear complementarity problem known to date, to provide a basis for the continued research on the non linear complementarityproblem, and to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Book
Numerical Optimization: Theoretical and Practical Aspects
TL;DR: This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied, and provides adequate examples to help the reader understand the methods better and explore possible pitfalls.
Journal ArticleDOI
Strategic gaming analysis for electric power systems: an MPEC approach
TL;DR: In this article, a single-firm game model for analyzing power markets is presented, where each generating firm submits bids to an ISO, choosing its bids to maximize profits subject to anticipated reactions by rival firms.
Journal ArticleDOI
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Holger Scheel,Stefan Scholtes +1 more
TL;DR: Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared and Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima are presented.