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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Contents

Exact Penalization of MPEC
61
FirstOrder Optimality Conditions
113
Verification of MPEC Hypotheses
145
SecondOrder Optimality Conditions
223
Algorithms for MPEC
271
Bibliography
361
Index
391
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