Mathematical programs with equilibrium constraints

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. 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 -- Provided by Publisher

an Extensive Study For An Important Class Of Constrained Optimisation Problems Known As Mathematical Programs With Equilibrium Constraints.

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an Extensive Study Of Mathematical Programs With Equilibrium Constraints (mpec) Providing A Solid Foundation In The Extensions Of Bilevel Optimization Problems. The Volume Describes Source Problems From Engineering And Economics, Error Bounds And Parametric Analysis As The Tools To Establish An Exact Penalization Theory, A Set Of Mpec Constraint Qualifications And The First- And Second-order Optimality Conditions, Iterative Algorithms, Implicit Programming Algorithm, And A Piecewise Sequential Quadratic Programming Algorithm For Mpecs. Annotation C. By Book News, Inc., Portland, Or.

Content: 1. Introduction -- 2. Exact Penalization of MPEC -- 3. First-Order Optimality Conditions -- 4. Verification of MPEC Hypotheses -- 5. Second-Order Optimality Conditions -- 6. Algorithms for MPEC.