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Annals of Operations Research

, Volume 240, Issue 1, pp 271–299 | Cite as

Merit functions: a bridge between optimization and equilibria

  • Massimo PappalardoEmail author
  • Giandomenico Mastroeni
  • Mauro Passacantando
SI: 4OR Surveys

Abstract

In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented.

Keywords

Merit functions Gap functions Variational inequalities Equilibrium problems Descent methods 

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Massimo Pappalardo
    • 1
    Email author
  • Giandomenico Mastroeni
    • 1
  • Mauro Passacantando
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

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