An Armijo-type method for pseudomonotone equilibrium problems and its applications

We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithm...

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Bibliographic Details
Published inJournal of global optimization Vol. 57; no. 3; pp. 803 - 820
Main Authors Anh, P. N., Le Thi, H. A.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Springer Nature B.V
Springer Verlag
Subjects
Algorithms
Computer Science
Convergence
Equilibrium
Inequalities
Laboratories
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Armijo-type method
65 K10
Global convergence
Equilibrium problems
90 C25
Pseudomonotone
Online AccessGet full text
ISSN0925-5001
1573-2916
DOI10.1007/s10898-012-9970-8

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Summary:We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9970-8