Equilibria and Complementarity Problems

  • Steven A. Gabriel
  • Antonio J. Conejo
  • J. David Fuller
  • Benjamin F. Hobbs
  • Carlos Ruiz
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 180)

Abstract

In this chapter, we explore the notions of equilibria and optimization and show how in some cases they are related. The notion of an equilibrium is a fundamental concept that has been used in a variety of disciplines such as economics, engineering, and science to name just a few. At its core, an equilibrium is a state of the system being modeled for which the system has no “incentive” to change. These incentives can be monetary in the case of economics or based on natural forces and scientific laws such as total input equals total output. Some well-known engineering examples include: conservation of energy, conservation of mass, conservation of momentum [8], steady-state probabilities in Markov chains such as birth-and-death processes [53] to name a few. These and other engineering examples are typified by a balancing of forces or conditions so that the state once reached will not easily (if at all) be left.

Keywords

Petroleum Transportation Drilling Expense Nash 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Steven A. Gabriel
    • 1
  • Antonio J. Conejo
    • 2
  • J. David Fuller
    • 3
  • Benjamin F. Hobbs
    • 4
  • Carlos Ruiz
    • 5
  1. 1.Department of Civil and Environmental EngineeringUniversity of MarylandCollege ParkUSA
  2. 2.University of Castilla – La ManchaCiudad RealSpain
  3. 3.Department of Management SciencesUniversity of WaterlooWaterlooCanada
  4. 4.Department of Geography and Environmental EngineeringThe Johns Hopkins UniversityBaltimoreUSA
  5. 5.European Foundation for New Energy – EDF École Centrale Paris and SupélecChâtenay-MalabryFrance

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