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

In: Optimization, Simulation, and Control

Author

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  • Ider Tseveendorj

    (University of Versailles)

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.

Suggested Citation

  • Ider Tseveendorj, 2013. "Mathematical Programs with Equilibrium Constraints: A Brief Survey of Methods and Optimality Conditions," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 49-61, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_4
    DOI: 10.1007/978-1-4614-5131-0_4
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    Cited by:

    1. Aussel, Didier & Cao Van, Kien & Salas, David, 2023. "Optimal design of exchange water networks with control inputs in Eco-Industrial Parks," Energy Economics, Elsevier, vol. 120(C).

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