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Mathematical Programs with Equilibrium Constraints: A Brief Survey of Methods and Optimality Conditions

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

Abstract

This chapter provides a short survey of the research for an important class of constrained optimization problems for which their constraints are defined in part by a variational inequality. Such problems are known as mathematical programs with equilibrium constraints (MPEC). MPEC arise naturally in different areas and play an important role, for example, in the pricing of telecommunication and transportation networks, in economic modeling, in computational mechanics in many other fields of modern optimization, and have been the subject of a number of recent studies. We present a general formulation of MPEC, describe the main characteristics of MPEC, and review the main properties and theoretical results for these problems. The short survey mainly concentrates on the review of the available solution methodology.

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Acknowledgements

This research was partly supported by the Agence Nationale de la Recherche under a grant HORUS and partly by the DIGITEO under a grant 2009-55D “ARM.”

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Authors and Affiliations

  1. Laboratory PRISM, Computer Science Department, University of Versailles, St.-Quentin-en-Yvelines, 45 avenue des États-Unis, 78035, Versailles Cedex, France

    Ider Tseveendorj

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  1. Ider Tseveendorj
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Correspondence to Ider Tseveendorj .

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Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Tseveendorj, I. (2013). Mathematical Programs with Equilibrium Constraints: A Brief Survey of Methods and Optimality Conditions. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_4

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