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05 Mar 2014
Merit functions: a bridge between optimization and equilibria
 Massimo Pappalardo,
 Giandomenico Mastroeni,
 Mauro Passacantando
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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, quasivariational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented.
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Within this Article
 Introduction
 Preliminaries
 Merit functions for variational inequalities
 Merit functions for quasivariational inequalities
 Merit functions for abstract equilibrium problems
 Concluding remarks
 References
 References
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 Title
 Merit functions: a bridge between optimization and equilibria
 Journal

4OR
Volume 12, Issue 1 , pp 133
 Cover Date
 20140301
 DOI
 10.1007/s1028801402565
 Print ISSN
 16194500
 Online ISSN
 16142411
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Merit functions
 Gap functions
 Variational inequalities
 Equilibrium problems
 Descent methods
 90C33
 90C30
 Authors

 Massimo Pappalardo ^{(1)}
 Giandomenico Mastroeni ^{(1)}
 Mauro Passacantando ^{(1)}
 Author Affiliations

 1. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127 , Pisa, Italy